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2-Source Dispersers for Sub-Polynomial Entropy and Ramsey Graphs Beating the Frankl-Wilson Construction

The main result of this paper is an explicit disperser for two independent sources on n bits, each of entropy k = n o(1). Put differently, setting N = 2n and K = 2k , we construct explicit N N Boolean matrices for which no K K sub-matrix is monochromatic. Viewed as adjacency matrices of bipartite graphs, this gives an explicit construction of K-Ramsey bipartite graphs of size N . This greatly improves the previous bound of k = o(n) of Barak, Kindler, Shaltiel, Sudakov and Wigderson [4]. It also significantly improves the 25-year record of k = ~ O(n) on the special case of Ramsey graphs, due to Frankl and Wilson [9]. The construction uses (besides "classical" extractor ideas) almost all of the machinery developed in the last couple of years for extraction from independent sources, including: Bourgain's extractor for 2 independent sources of some entropy rate < 1/2 [5] Raz's extractor for 2 independent sources, one of which has any entropy rate > 1/2 [18] Rao's extractor for 2 independent block-sources of entropy n (1) [17] The "Challenge-Response" mechanism for detecting "entropy concentration" of [4]. The main novelty comes in a bootstrap procedure which allows the Challenge-Response mechanism of [4] to be used with sources of less and less entropy, using recursive calls to itself. Subtleties arise since the success of this mechanism depends on restricting the given sources, and so recursion constantly changes the original sources. These are resolved via a new construct, in between a disperser and an extractor, which behaves like an extractor on sufficiently large subsources of the given ones. This version is only an extended abstract, please see the full version, available on the authors' homepages, for more details.

INTRODUCTION This paper deals with randomness extraction from weak random sources. Here a weak random source is a distribution which contains some entropy. The extraction task is to design efficient algorithms (called extractors) to convert this entropy into useful form, namely a sequence of independent unbiased bits. Beyond the obvious motivations (potential use of physical sources in pseudorandom generators and in derandomization), extractors have found applications in a variety of areas in theoretical computer science where randomness does not seem an issue, such as in efficient constructions of communication networks [24, 7], error correcting codes [22, 12], data structures [14] and more. Most work in this subject over the last 20 years has focused on what is now called seeded extraction, in which the extractor is given as input not only the (sample from the) defective random source, but also a few truly random bits (called the seed). A comprehensive survey of much of this body of work is [21]. Another direction, which has been mostly dormant till about two years ago, is (seedless, deterministic) extraction from a few independent weak sources. This kind of extraction is important in several applications where it is unrealis-tic to have a short random seed or deterministically enumerate over its possible values. However, it is easily shown to be impossible when only one weak source is available. When at least 2 independent sources are available extraction becomes possible in principle. The 2-source case is the one we will focus on in this work. The rest of the introduction is structured as follows. We'll start by describing our main result in the context of Ramsey graphs. We then move to the context of extractors and disperser , describing the relevant background and stating our result in this language. Then we give an overview of the construction of our dispersers, describing the main building blocks we construct along the way. As the construction is quite complex and its analysis quite subtle, in this proceedings version we try to abstract away many of the technical difficulties so that the main ideas, structure and tools used are highlighted. For that reason we also often state definitions and theorems somewhat informally. 1.1 Ramsey Graphs Definition 1.1. A graph on N vertices is called a K-Ramsey Graph if it contains no clique or independent set of size K. In 1947 Erd os published his paper inaugurating the Prob-abilistic Method with a few examples, including a proof that most graphs on N = 2 n vertices are 2n-Ramsey. The quest for constructing such graphs explicitly has existed ever since and lead to some beautiful mathematics. The best record to date was obtained in 1981 by Frankl and Wilson [9], who used intersection theorems for set systems to construct N -vertex graphs which are 2 n log n -Ramsey. This bound was matched by Alon [1] using the Polynomial Method, by Grolmusz [11] using low rank matrices over rings, and also by Barak [2] boosting Abbot's method with almost k-wise independent random variables (a construction that was independently discovered by others as well). Remark-ably all of these different approaches got stuck at essentially the same bound. In recent work, Gopalan [10] showed that other than the last construction, all of these can be viewed as coming from low-degree symmetric representations of the OR function. He also shows that any such symmetric representation cannot be used to give a better Ramsey graph, which gives a good indication of why these constructions had similar performance. Indeed, as we will discuss in a later section, the n entropy bound initially looked like a natural obstacle even for our techniques, though eventually we were able to surpass it. The analogous question for bipartite graphs seemed much harder. Definition 1.2. A bipartite graph on two sets of N vertices is a K-Ramsey Bipartite Graph if it has no K K complete or empty bipartite subgraph. While Erd os' result on the abundance of 2n-Ramsey graphs holds as is for bipartite graphs, until recently the best explicit construction of bipartite Ramsey graphs was 2 n/2 Ramsey , using the Hadamard matrix. This was improved last year, first to o(2 n/2 ) by Pudlak and R odl [16] and then to 2 o(n) by Barak, Kindler, Shaltiel, Sudakov and Wigderson [4]. It is convenient to view such graphs as functions f : ({0, 1} n ) 2 {0, 1}. This then gives exactly the definition of a disperser. Definition 1.3. A function f : ({0, 1} n ) 2 {0, 1} is called a 2-source disperser for entropy k if for any two sets X, Y {0, 1} n with |X| = |Y | = 2 k , we have that the image f (X, Y ) is {0, 1}. This allows for a more formal definition of explicitness: we simply demand that the function f is computable in polynomial time. Most of the constructions mentioned above are explicit in this sense. 1 Our main result (stated informally) significantly improves the bounds in both the bipartite and non-bipartite settings: Theorem 1.4. For every N we construct polynomial time computable bipartite graphs which are 2 n o (1) -Ramsey. A standard transformation of these graphs also yields polynomial time computable ordinary Ramsey Graphs with the same parameters . 1.2 Extractors and Dispersers from independent sources Now we give a brief review of past relevant work (with the goal of putting this paper in proper context) and describe some of the tools from these past works that we will use. We start with the basic definitions of k-sources by Nisan and Zuckerman [15] and of extractors and dispersers for independent sources by Santha and Vazirani [20]. Definition 1.5 ([15], see also [8]). The min-entropy of a distribution X is the maximum k such that for every element x in its support, Pr[X = x] 2 -k . If X is a distribution on strings with min-entropy at least k, we will call X a k-source 2 . To simplify the presentation, in this version of the paper we will assume that we are working with entropy as opposed to min-entropy. Definition 1.6 ([20]). A function f : ({0, 1} n ) c {0, 1} m is a c-source (k, ) extractor if for every family of c independent k-sources X 1 , , X c , the output f (X 1 , , X c ) 1 The Abbot's product based Ramsey-graph construction of [3] and the bipartite Ramsey construction of [16] only satisfy a weaker notion of explicitness. 2 It is no loss of generality to imagine that X is uniformly distributed over some (unknown) set of size 2 k . 672 is a -close 3 to uniformly distributed on m bits. f is a disperser for the same parameters if the output is simply required to have a support of relative size (1 - ). To simplify the presentation, in this version of the paper, we will assume that = 0 for all of our constructions. In this language, Erd os' theorem says that most functions f : ({0, 1} n ) 2 {0,1} are dispersers for entropy 1 + log n (treating f as the characteristic function for the set of edges of the graph). The proof easily extends to show that indeed most such functions are in fact extractors. This naturally challenges us to find explicit functions f that are 2-source extractors. Until one year ago, essentially the only known explicit construction was the Hadamard extractor Had defined by Had (x, y) = x, y ( mod 2). It is an extractor for entropy k > n/2 as observed by Chor and Goldreich [8] and can be extended to give m = (n) output bits as observed by Vazirani [23]. Over 20 years later, a recent breakthrough of Bourgain [5] broke this "1/2 barrier" and can handle 2 sources of entropy .4999n, again with linear output length m = (n). This seemingly minor improvement will be crucial for our work! Theorem 1.7 ([5]). There is a polynomial time computable 2-source extractor f : ({0, 1} n ) 2 {0, 1} m for entropy .4999n and m = (n). No better bounds are known for 2-source extractors. Now we turn our attention to 2-source dispersers. It turned out that progress for building good 2-source dispersers came via progress on extractors for more than 2 sources, all happening in fast pace in the last 2 years. The seminal paper of Bourgain , Katz and Tao [6] proved the so-called "sum-product theorem" in prime fields, a result in arithmetic combinatorics . This result has already found applications in diverse areas of mathematics, including analysis, number theory, group theory and ... extractor theory. Their work implic-itly contained dispersers for c = O(log(n/k)) independent sources of entropy k (with output m = (k)). The use of the "sum-product" theorem was then extended by Barak et al. [3] to give extractors with similar parameters. Note that for linear entropy k = (n), the number of sources needed for extraction c is a constant! Relaxing the independence assumptions via the idea of repeated condensing, allowed the reduction of the number of independent sources to c = 3, for extraction from sources of any linear entropy k = (n), by Barak et al. [4] and independently by Raz [18]. For 2 sources Barak et al. [4] were able to construct dispersers for sources of entropy o(n). To do this, they first showed that if the sources have extra structure (block-source structure, defined below), even extraction is possible from 2 sources. The notion of block-sources, capturing "semi inde-pendence" of parts of the source, was introduced by Chor and Goldreich [8]. It has been fundamental in the development of seeded extractors and as we shall see, is essential for us as well. Definition 1.8 ([8]). A distribution X = X 1 , . . . , X c is a c-block-source of (block) entropy k if every block X i has entropy k even conditioned on fixing the previous blocks X 1 , , X i-1 to arbitrary constants. 3 The error is usually measured in terms of 1 distance or variation distance. This definition allowed Barak et al. [4] to show that their extractor for 4 independent sources, actually performs as well with only 2 independent sources, as long as both are 2-block-sources. Theorem 1.9 ([4]). There exists a polynomial time computable extractor f : ({0, 1} n ) 2 {0, 1} for 2 independent 2-block-sources with entropy o(n). There is no reason to assume that the given sources are block-sources, but it is natural to try and reduce to this case. This approach has been one of the most successful in the extractor literature. Namely try to partition a source X into two blocks X = X 1 , X 2 such that X 1 , X 2 form a 2-block-source. Barak et al. introduced a new technique to do this reduction called the Challenge-Response mechanism, which is crucial for this paper. This method gives a way to "find" how entropy is distributed in a source X, guiding the choice of such a partition. This method succeeds only with small probability, dashing the hope for an extractor, but still yielding a disperser. Theorem 1.10 ([4]). There exists a polynomial time computable 2-source disperser f : ({0, 1} n ) 2 {0, 1} for entropy o(n). Reducing the entropy requirement of the above 2-source disperser, which is what we achieve in this paper, again needed progress on achieving a similar reduction for extractors with more independent sources. A few months ago Rao [?] was able to significantly improve all the above results for c 3 sources. Interestingly, his techniques do not use arithmetic combinatorics, which seemed essential to all the papers above. He improves the results of Barak et al. [3] to give c = O((log n)/(log k))-source extractors for entropy k. Note that now the number c of sources needed for extraction is constant, even when the entropy is as low as n for any constant ! Again, when the input sources are block-sources with sufficiently many blocks, Rao proves that 2 independent sources suffice (though this result does rely on arithmetic combinatorics , in particular, on Bourgain's extractor). Theorem 1.11 ([?]). There is a polynomial time computable extractor f : ({0, 1} n ) 2 {0, 1} m for 2 independent c-block-sources with block entropy k and m = (k), as long as c = O((log n)/(log k)). In this paper (see Theorem 2.7 below) we improve this result to hold even when only one of the 2 sources is a c-block -source. The other source can be an arbitrary source with sufficient entropy. This is a central building block in our construction. This extractor, like Rao's above, critically uses Bourgain's extractor mentioned above. In addition it uses a theorem of Raz [18] allowing seeded extractors to have "weak" seeds, namely instead of being completely random they work as long as the seed has entropy rate > 1/2. MAIN NOTIONS AND NEW RESULTS The main result of this paper is a polynomial time computable disperser for 2 sources of entropy n o(1) , significantly improving both the results of Barak et al. [4] (o(n) entropy). It also improves on Frankl and Wilson [9], who only built Ramsey Graphs and only for entropy ~ O(n). 673 Theorem 2.1 (Main theorem, restated). There exists a polynomial time computable 2-source disperser D : ({0, 1} n ) 2 {0, 1} for entropy n o(1) . The construction of this disperser will involve the construction of an object which in some sense is stronger and in another weaker than a disperser: a subsource somewhere extractor. We first define a related object: a somewhere extractor , which is a function producing several outputs, one of which must be uniform. Again we will ignore many technical issues such as error, min-entropy vs. entropy and more, in definitions and results, which are deferred to the full version of this paper. Definition 2.2. A function f : ({0, 1} n ) 2 ({0, 1} m ) is a 2-source somewhere extractor with outputs, for entropy k, if for every 2 independent k-sources X, Y there exists an i [] such the ith output f(X,Y ) i is a uniformly distributed string of m bits. Here is a simple construction of such a somewhere extractor with as large as poly(n) (and the p in its name will stress the fact that indeed the number of outputs is that large). It will nevertheless be useful to us (though its description in the next sentence may be safely skipped). Define pSE (x, y) i = V(E(x, i), E(y, i)) where E is a "strong" logarithmic seed extractor, and V is the Hadamard/Vazirani 2-source extractor. Using this construction, it is easy to see that: Proposition 2.3. For every n, k there is a polynomial time computable somewhere extractor pSE : ({0, 1} n ) 2 ({0, 1} m ) with = poly(n) outputs, for entropy k, and m = (k). Before we define subsource somewhere extractor, we must first define a subsource. Definition 2.4 (Subsources). Given random variables Z and ^ Z on {0, 1} n we say that ^ Z is a deficiency d subsource of Z and write ^ Z Z if there exists a set A {0,1} n such that (Z|Z A) = ^Z and Pr[Z A] 2 -d . A subsource somewhere extractor guarantees the "some-where extractor" property only on subsources X , Y of the original input distributions X, Y (respectively). It will be extremely important for us to make these subsources as large as possible (i.e. we have to lose as little entropy as possible). Controlling these entropy deficiencies is a major technical complication we have to deal with. However we will be informal with it here, mentioning it only qualitatively when needed. We discuss this issue a little more in Section 6. Definition 2.5. A function f : ({0, 1} n ) 2 ({0, 1} m ) is a 2-source subsource somewhere extractor with outputs for entropy k, if for every 2 independent k-sources X, Y there exists a subsource ^ X of X, a subsource ^ Y of Y and an i [] such the i th output f ( ^ X, ^ Y ) i is a uniformly distributed string of m bits. A central technical result for us is that with this "sub-source" relaxation, we can have much fewer outputs indeed we'll replace poly(n) outputs in our first construction above with n o(1) outputs. Theorem 2.6 (Subsource somewhere extractor). For every > 0 there is a polynomial time computable subsource somewhere extractor SSE : ({0, 1} n ) 2 ({0,1} m ) with = n o(1) outputs, for entropy k = n , with output m = k. We will describe the ideas used for constructing this important object and analyzing it in the next section, where we will also indicate how it is used in the construction of the final disperser. Here we state a central building block, mentioned in the previous section (as an improvement of the work of Rao [?]). We construct an extractor for 2 independent sources one of which is a block-sources with sufficient number of blocks. Theorem 2.7 (Block Source Extractor). There is a polynomial time computable extractor B : ({0, 1} n ) 2 {0, 1} m for 2 independent sources, one of which is a c-block-sources with block entropy k and the other a source of entropy k, with m = (k), and c = O((log n)/(log k)). A simple corollary of this block-source extractor B, is the following weaker (though useful) somewhere block-source extractor SB. A source Z = Z 1 , Z 2 , , Z t is a somewhere c-block-source of block entropy k if for some c indices i 1 < i 2 < < i c the source Z i 1 , Z i 2 , , Z i c is a c-block-source. Collecting the outputs of B on every c-subset of blocks results in that somewhere extractor. Corollary 2.8. There is a polynomial time computable somewhere extractor SB : ({0, 1} n ) 2 ({0, 1} m ) for 2 independent sources, one of which is a somewhere c-block-sources with block entropy k and t blocks total and the other a source of entropy k, with m = (k), c = O((log n)/(log k)), and t c . In both the theorem and corollary above, the values of entropy k we will be interested in are k = n (1) . It follows that a block-source with a constant c = O(1) suffices. THE CHALLENGE-RESPONSE MECHANISM We now describe abstractly a mechanism which will be used in the construction of the disperser as well as the subsource somewhere extractor. Intuitively, this mechanism allows us to identify parts of a source which contain large amounts of entropy. One can hope that using such a mechanism one can partition a given source into blocks in a way which make it a block-source, or alternatively focus on a part of the source which is unusually condensed with entropy two cases which may simplify the extraction problem. The reader may decide, now or in the middle of this section, to skip ahead to the next section which describes the construction of the subsource somewhere extractor SSE, which extensively uses this mechanism. Then this section may seem less abstract, as it will be clearer where this mechanism is used. This mechanism was introduced by Barak et al. [4], and was essential in their 2-source disperser. Its use in this paper is far more involved (in particular it calls itself recursively, a fact which creates many subtleties). However, at a high level, the basic idea behind the mechanism is the same: Let Z be a source and Z a part of Z (Z projected on a subset of the coordinates). We know that Z has entropy k, 674 and want to distinguish two possibilities: Z has no entropy (it is fixed) or it has at least k entropy. Z will get a pass or fail grade, hopefully corresponding to the cases of high or no entropy in Z . Anticipating the use of this mechanism, it is a good idea to think of Z as a "parent" of Z , which wants to check if this "child" has sufficient entropy. Moreover, in the context of the initial 2 sources X, Y we will operate on, think of Z as a part of X, and thus that Y is independent of Z and Z . To execute this "test" we will compute two sets of strings (all of length m, say): the Challenge C = C(Z , Y ) and the Response R = R(Z, Y ). Z fails if C R and passes otherwise. The key to the usefulness of this mechanism is the following lemma, which states that what "should" happen, indeed happens after some restriction of the 2 sources Z and Y . We state it and then explain how the functions C and R are defined to accommodate its proof. Lemma 3.1. Assume Z, Y are sources of entropy k. 1. If Z has entropy k + O(m), then there are subsources ^ Z of Z and ^ Y of Y , such that Pr[ ^ Z passes] = Pr[C( ^ Z , ^ Y ) R ( ^ Z, ^ Y )] 1-n O(1) 2 -m 2. If Z is fixed (namely, has zero entropy), then for some subsources ^ Z of Z and ^ Y of Y , we have Pr[Z fails] = Pr[C( ^ Z , ^ Y ) R( ^Z, ^Y)] = 1 Once we have such a mechanism, we will design our disperser algorithm assuming that the challenge response mechanism correctly identifies parts of the source with high or low levels of entropy. Then in the analysis, we will ensure that our algorithm succeeds in making the right decisions, at least on subsources of the original input sources. Now let us explain how to compute the sets C and R. We will use some of the constructs above with parameters which don't quite fit. The response set R(Z, Y ) = pSE(Z, Y ) is chosen to be the output of the somewhere extractor of Proposition 2.3. The challenge set C(Z , Y ) = SSE(Z , Y ) is chosen to be the output of the subsource somewhere extractor of Theorem 2.6. Why does it work? We explain each of the two claims in the lemma in turn (and after each comment on the important parameters and how they differ from Barak et al. [4]). 1. Z has entropy. We need to show that Z passes the test with high probability. We will point to the output string in C( ^ Z , ^ Y ) which avoids R( ^ Z, ^ Y ) with high probability as follows. In the analysis we will use the union bound on several events, one associated with each (poly(n) many) string in pSE( ^ Z, ^ Y ). We note that by the definition of the response function, if we want to fix a particular element in the response set to a particular value, we can do this by fixing E(Z, i) and E (Y, i). This fixing keeps the restricted sources independent and loses only O(m) entropy. In the subsource of Z guaranteed to exist by Theorem 2.6 we can afford to lose this entropy in Z . Thus we conclude that one of its outputs is uniform. The probability that this output will equal any fixed value is thus 2 -m , completing the argument. We note that we can handle the polynomial output size of pSE, since the uniform string has length m = n (1) (something which could not be done with the technology available to Barak et al. [4]). 2. Z has no entropy. We now need to guarantee that in the chosen subsources (which we choose) ^ Z, ^ Y , all strings in C = C( ^ Z , ^ Y ) are in R( ^ Z, ^ Y ). First notice that as Z is fixed, C is only a function of Y . We set ~ Y to be the subsource of Y that fixes all strings in C = C(Y ) to their most popular values (losing only m entropy from Y ). We take care of including these fixed strings in R(Z, ~ Y ) one at a time, by restricting to subsources assuring that. Let be any m-bit string we want to appear in R(Z, ~ Y ). Recall that R (z, y) = V(E(z, i), E(y, i)). We pick a "good" seed i, and restrict Z, ~ Y to subsources with only O(m) less entropy by fixing E(Z, i) = a and E( ~ Y , i) = b to values (a, b) for which V(a, b) = . This is repeated suc-cessively times, and results in the final subsources ^ Z, ^ Y on which ^ Z fails with probability 1. Note that we keep reducing the entropy of our sources times, which necessitates that this be tiny (here we could not tolerate poly(n), and indeed can guarantee n o(1) , at least on a subsource this is one aspect of how crucial the subsource somewhere extractor SSE is to the construction. We note that initially it seemed like the Challenge-Response mechanism as used in [4] could not be used to handle entropy that is significantly less than n (which is approxi-mately the bound that many of the previous constructions got stuck at). The techniques of [4] involved partitioning the sources into t pieces of length n/t each, with the hope that one of those parts would have a significant amount of entropy, yet there'd be enough entropy left over in the rest of the source (so that the source can be partitioned into a block source). However it is not clear how to do this when the total entropy is less than n. On the one hand we will have to partition our sources into blocks of length significantly more than n (or the adversary could distribute a negligible fraction of entropy in all blocks). On the other hand, if our blocks are so large, a single block could contain all the entropy. Thus it was not clear how to use the challenge response mechanism to find a block source. THE SUBSOURCE SOMEWHERE EXTRACTOR SSE We now explain some of the ideas behind the construction of the subsource somewhere extractor SSE of Theorem 2.6. Consider the source X. We are seeking to find in it a somewhere c-block-source, so that we can use it (together with Y ) in the block-source extractor of Theorem 2.8. Like in previous works in the extractor literature (e.g. [19, 13]) we use a "win-win" analysis which shows that either X is already a somewhere c-block-source, or it has a condensed part which contains a lot of the entropy of the source. In this case we proceed recursively on that part. Continuing this way we eventually reach a source so condensed that it must be a somewhere block source. Note that in [4], the challenge response mechanism was used to find a block source also, but there the entropy was so high that they could afford to use 675 t blocks low high med n bits total t blocks med med low high responded Challenge Challenge responded Challenge Unresponded med med n/t bits total SB SB Outputs Somewhere Block Source! Not Somewhere block source X Random Row < k' 0< low < k'/t k'/c < high < k' k'/t < med < k'/c Figure 1: Analysis of the subsource somewhere extractor. a tree of depth 1. They did not need to recurse or condense the sources. Consider the tree of parts of the source X evolved by such recursion. Each node in the tree corresponds to some interval of bit locations of the source, with the root node corresponding to the entire source. A node is a child of another if its interval is a subinterval of the parent. It can be shown that some node in the tree is "good"; it corresponds to a somewhere c-source, but we don't know which node is good. Since we only want a somewhere extractor, we can apply to each node the somewhere block-source extractor of Corollary 2.8 this will give us a random output in every "good" node of the tree. The usual idea is output all these values (and in seeded extractors, merge them using the ex-ternally given random seed). However, we cannot afford to do that here as there is no external seed and the number of these outputs (the size of the tree) is far too large. Our aim then will be to significantly prune this number of candidates and in fact output only the candidates on one path to a canonical "good" node. First we will give a very informal description of how to do this (Figure 1). Before calling SSE recursively on a subpart of a current part of X, we'll use the "Challenge-Response" mechanism described above to check if "it has entropy". 4 We will recurse only with the first (in left-to-right order) part which passes the "entropy test". Thus note that we will follow a single path on this tree. The algorithm SSE will output only the sets of strings produced by applying the somewhere c-block-extractor SB on the parts visited along this path. Now let us describe the algorithm for SSE. SSE will be initially invoked as SSE(x, y), but will recursively call itself with different inputs z which will always be substrings of x. 4 We note that we ignore the additional complication that SSE will actually use recursion also to compute the challenge in the challenge-response mechanism. Algorithm: SSE (z, y) Let pSE(., .) be the somewhere extractor with a polynomial number of outputs of Proposition 2.3. Let SB be the somewhere block source extractor of Corollary 2.8. Global Parameters: t, the branching factor of the tree. k the original entropy of the sources. Output will be a set of strings. 1. If z is shorter than k, return the empty set, else continue. 2. Partition z into t equal parts z = z 1 , z 2 , . . . , z t . 3. Compute the response set R(z, y) which is the set of strings output by pSE(z, y). 4. For i [t], compute the challenge set C(z i , y), which is the set of outputs of SSE(z i , y). 5. Let h be the smallest index for which the challenge set C (z h , y) is not contained in the response set (set h = t if no such index exists). 6. Output SB(z, y) concatenated with SSE(z h , y). Proving that indeed there are subsources on which SSE will follow a path to a "good" (for these subsources) node, is the heart of the analysis. It is especially complex due to the fact that the recursive call to SSE on subparts of the current part is used to generate the Challenges for the Challenge-Response mechanism. Since SSE works only on a subsources we have to guarantee that restriction to these does not hamper the behavior of SSE in past and future calls to it. Let us turn to the highlights of the analysis, for the proof of Theorem 2.6. Let k be the entropy of the source Z at some place in this recursion. Either one of its blocks Z i has 676 entropy k /c, in which case it is very condensed, since its size is n/t for t c), or it must be that c of its blocks form a c-block source with block entropy k /t (which is sufficient for the extractor B used by SB). In the 2nd case the fact that SB(z, y) is part of the output of of our SSE guarantees that we are somewhere random. If the 2nd case doesn't hold, let Z i be the leftmost condensed block. We want to ensure that (on appropriate subsources) SSE calls itself on that ith subpart. To do so, we fix all Z j for j < i to constants z j . We are now in the position described in the Challenge-Response mechanism section, that (in each of the first i parts) there is either no entropy or lots of entropy. We further restrict to subsources as explained there which make all first i - 1 blocks fail the "entropy test", and the fact that Z i still has lots of entropy after these restrictions (which we need to prove) ensures that indeed SSE will be recursively applied to it. We note that while the procedure SSE can be described recursively , the formal analysis of fixing subsources is actually done globally, to ensure that indeed all entropy requirements are met along the various recursive calls. Let us remark on the choice of the branching parameter t. On the one hand, we'd like to keep it small, as it dominates the number of outputs t c of SB, and thus the total number of outputs (which is t c log t n). For this purpose, any t = n o(1) will do. On the other hand, t should be large enough so that condensing is faster than losing entropy. Here note that if Z is of length n, its child has length n/t, while the entropy shrinks only from k to k /c. A simple calculation shows that if k (log t)/ log c) > n 2 then a c block-source must exist along such a path before the length shrinks to k. Note that for k = n (1) a (large enough) constant t suffices (resulting in only logarithmic number of outputs of SSE). This analysis is depicted pictorially in Figure 1. THE FINAL DISPERSER D Following is a rough description of our disperser D proving Theorem 2.1. The high level structure of D will resemble the structure of SSE - we will recursively split the source X and look for entropy in the parts. However now we must output a single value (rather than a set) which can take both values 0 and 1. This was problematic in SSE, even knowing where the "good" part (containing a c-block-source) was! How can we do so now? We now have at our disposal a much more powerful tool for generating challenges (and thus detecting entropy), namely the subsource somewhere disperser SSE. Note that in constructing SSE we only had essentially the somewhere c-block-source extractor SB to (recursively) generate the challenges, but it depended on a structural property of the block it was applied on. Now SSE does not assume any structure on its input sources except sufficient entropy 5 . Let us now give a high level description of the disperser D . It too will be a recursive procedure. If when processing some part Z of X it "realizes" that a subpart Z i of Z has entropy, but not all the entropy of Z (namely Z i , Z is a 2-block-source) then we will halt and produce the output of D. Intuitively, thinking about the Challenge-Response mechanism described above, the analysis implies that we 5 There is a catch it only works on subsources of them! This will cause us a lot of head ache; we will elaborate on it later. can either pass or fail Z i (on appropriate subsources). But this means that the outcome of this "entropy test" is a 1-bit disperser! To capitalize on this idea, we want to use SSE to identify such a block-source in the recursion tree. As before, we scan the blocks from left to right, and want to distinguish three possibilities. low Z i has low entropy. In this case we proceed to i + 1. medium Z i has "medium" entropy (Z i , Z is a block-source). In which case we halt and produce an output (zero or one). high Z i has essentially all entropy of Z. In this case we recurse on the condensed block Z i . As before, we use the Challenge-Response mechanism (with a twist). We will compute challenges C(Z i , Y ) and responses R (Z, Y ), all strings of length m. The responses are computed exactly as before, using the somewhere extractor pSE. The Challenges are computed using our subsource somewhere extractor SSE. We really have 4 possibilities to distinguish, since when we halt we also need to decide which output bit we give. We will do so by deriving three tests from the above challenges and responses: (C H , R H ), (C M , R M ), (C L , R L ) for high, medium and low respectively, as follows. Let m m H >> m M >> m L be appropriate integers: then in each of the tests above we restrict ourselves to prefixes of all strings of the appropriate lengths only. So every string in C M will be a prefix of length m M of some string in C H . Similarly, every string in R L is the length m L prefix of some string in R H . Now it is immediately clear that if C M is contained in R M , then C L is contained in R L . Thus these tests are monotone, if our sample fails the high test, it will definitely fail all tests. Algorithm: D (z, y) Let pSE(., .) be the somewhere extractor with a polynomial number of outputs of Proposition 2.3. Let SSE(., .) be the subsource somewhere extractor of Theorem 2.6. Global Parameters: t, the branching factor of the tree. k the original entropy of the sources. Local Parameters for recursive level: m L m M m H . Output will be an element of {0, 1}. 1. If z is shorter than k, return 0. 2. Partition z into t equal parts z = z 1 , z 2 , . . . , z t . 3. Compute three response sets R L , R M , R H using pSE(z, y). R j will be the prefixes of length m j of the strings in pSE (z, y). 4. For each i [t], compute three challenge sets C i L , C i M , C i H using SSE(z i , y). C i j will be the prefixes of length m j of the strings in SSE(z i , y). 5. Let h be the smallest index for which the challenge set C L is not contained in the response set R L , if there is no such index, output 0 and halt. 6. If C h H is contained in R H and C h H is contained in R M , output 0 and halt. If C h H is contained in R H but C h H is not contained in R M , output 1 and halt. 677 t blocks t blocks t blocks fail fail fail pass pass pass fail fail fail fail fail fail fail fail fail fail fail fail pass pass fail pass fail fail low low high low low low high low med n bits total n/t bits total X low low Output 0 Output 1 n/t^2 bits total X_3 (X_3)_4 Figure 2: Analysis of the disperser. 7. Output D(z h , y), First note the obvious monotonicity of the tests. If Z i fails one of the tests it will certainly fail for shorter strings. Thus there are only four outcomes to the three tests, written in the order (low, medium, high): (pass, pass, pass), (pass, pass, fail), (pass, fail, fail) and (fail, fail, fail). Conceptually, the algorithm is making the following decisions using the four tests: 1. (fail, fail, fail): Assume Z i has low entropy and proceed to block i + 1. 2. (pass, fail, fail): Assume Z i is medium, halt and output 0. 3. (pass, pass, fail): Assume Z i is medium, halt and output 1. 4. (pass, pass, pass): Assume Z i is high and recurse on Z i . The analysis of this idea (depicted in Figure 2).turns out to be more complex than it seems. There are two reasons for that. Now we briefly explain them and the way to overcome them in the construction and analysis. The first reason is the fact mentioned above, that SSE which generates the challenges, works only on a subsources of the original sources. Restricting to these subsources at some level of the recursion (as required by the analysis of of the test) causes entropy loss which affects both definitions (such as these entropy thresholds for decisions) and correct-ness of SSE in higher levels of recursion. Controlling this entropy loss is achieved by calling SSE recursively with smaller and smaller entropy requirements, which in turn limits the entropy which will be lost by these restrictions. In order not to lose all the entropy for this reason alone, we must work with special parameters of SSE, essentially requiring that at termination it has almost all the entropy it started with. The second reason is the analysis of the test when we are in a medium block. In contrast with the above situation, we cannot consider the value of Z i fixed when we need it to fail on the Medium and Low tests. We need to show that for these two tests (given a pass for High), they come up both (pass, fail) and (fail, fail) each with positive probability. Since the length of Medium challenges and responses is m M , the probability of failure is at least exp(-(m M )) (this follows relatively easily from the fact that the responses are somewhere random). If the Medium test fails so does the Low test, and thus (fail, fail) has a positive probability and our disperser D outputs 0 with positive probability. To bound (pass, fail) we first observe (with a similar reasoning) that the low test fails with probability at least exp(-(m L )). But we want the medium test to pass at the same time. This probability is at least the probability that low fails minus the probability that medium fails. We already have a bound on the latter: it is at most poly(n)exp(-m M ). Here comes our control of the different length into play - we can make the m L sufficiently smaller than m M to yield this difference positive. We conclude that our disperser D outputs 1 with positive probability as well. Finally, we need to take care of termination: we have to ensure that the recurrence always arrives at a medium subpart , but it is easy to chose entropy thresholds for low, medium and high to ensure that this happens. 678 RESILIENCY AND DEFICIENCY In this section we will breifly discuss an issue which arises in our construction that we glossed over in the previous sections . Recall our definition of subsources: Definition 6.1 (Subsources). Given random variables Z and ^ Z on {0, 1} n we say that ^ Z is a deficiency d subsource of Z and write ^ Z Z if there exists a set A {0,1} n such that (Z|A) = ^Z and Pr[Z A] 2 -d . Recall that we were able to guarantee that our algorithms made the right decisions only on subsources of the original source. For example, in the construction of our final disperser , to ensure that our algorithms correctly identify the right high block to recurse on, we were only able to guarantee that there are subsources of the original sources in which our algorithm makes the correct decision with high probability. Then, later in the analysis we had to further restrict the source to even smaller subsources. This leads to complications, since the original event of picking the correct high block, which occurred with high probability, may become an event which does not occur with high probability in the current subsource. To handle these kinds of issues, we will need to be very careful in measuring how small our subsources are. In the formal analysis we introduce the concept of resiliency to deal with this. To give an idea of how this works, here is the actual definition of somewhere subsource extractor that we use in the formal analysis. Definition 6.2 (subsource somewhere extractor). A function SSE : {0, 1} n {0, 1} n ({0, 1} m ) is a subsource somewhere extractor with nrows output rows, entropy threshold k, deficiency def, resiliency res and error if for every (n, k)-sources X, Y there exist a deficiency def subsource X good of X and a deficiency def subsource Y good of Y such that for every deficiency res subsource X of X good and deficiency res subsource Y of Y good , the random variable SSE(X , Y ) is -close to a m somewhere random distribution. It turns out that our subsource somewhere extractor does satisfy this stronger definition. The advantage of this definition is that it says that once we restrict our attention to the good subsources X good , Y good , we have the freedom to further restrict these subsources to smaller subsources, as long as our final subsources do not lose more entropy than the resiliency permits. This issue of managing the resiliency for the various objects that we construct is one of the major technical challenges that we had to overcome in our construction. OPEN PROBLEMS Better Independent Source Extractors A bottleneck to improving our disperser is the block versus general source extractor of Theorem 2.7. A good next step would be to try to build an extractor for one block source (with only a constant number of blocks) and one other independent source which works for polylog-arithmic entropy, or even an extractor for a constant number of sources that works for sub-polynomial entropy . Simple Dispersers While our disperser is polynomial time computable, it is not as explicit as one might have hoped. For instance the Ramsey Graph construction of Frankl-Wilson is extremely simple: For a prime p, let the vertices of the graph be all subsets of [p 3 ] of size p 2 - 1. Two vertices S,T are adjacent if and only if |S T| -1 mod p. It would be nice to find a good disperser that beats the Frankl-Wilson construction, yet is comparable in simplicity. REFERENCES [1] N. Alon. The shannon capacity of a union. Combinatorica, 18, 1998. [2] B. Barak. A simple explicit construction of an n ~ o(log n) -ramsey graph. Technical report, Arxiv, 2006. http://arxiv.org/abs/math.CO/0601651 . [3] B. Barak, R. Impagliazzo, and A. Wigderson. Extracting randomness using few independent sources. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pages 384393, 2004. [4] B. Barak, G. Kindler, R. Shaltiel, B. Sudakov, and A. Wigderson. Simulating independence: New constructions of condensers, Ramsey graphs, dispersers, and extractors. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pages 110, 2005. [5] J. Bourgain. More on the sum-product phenomenon in prime fields and its applications. International Journal of Number Theory, 1:132, 2005. [6] J. Bourgain, N. Katz, and T. Tao. A sum-product estimate in finite fields, and applications. Geometric and Functional Analysis, 14:2757, 2004. [7] M. Capalbo, O. Reingold, S. Vadhan, and A. Wigderson. Randomness conductors and constant-degree lossless expanders. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pages 659668, 2002. [8] B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM Journal on Computing, 17(2):230261, 1988. [9] P. Frankl and R. M. Wilson. Intersection theorems with geometric consequences. Combinatorica, 1(4):357368, 1981. [10] P. Gopalan. Constructing ramsey graphs from boolean function representations. In Proceedings of the 21th Annual IEEE Conference on Computational Complexity, 2006. [11] V. Grolmusz. Low rank co-diagonal matrices and ramsey graphs. Electr. J. Comb, 7, 2000. [12] V. Guruswami. Better extractors for better codes? Electronic Colloquium on Computational Complexity (ECCC), (080), 2003. [13] C. J. Lu, O. Reingold, S. Vadhan, and A. Wigderson. Extractors: Optimal up to constant factors. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing, pages 602611, 2003. [14] P. Miltersen, N. Nisan, S. Safra, and A. Wigderson. On data structures and asymmetric communication complexity. Journal of Computer and System Sciences, 57:3749, 1 1998. 679 [15] N. Nisan and D. Zuckerman. More deterministic simulation in logspace. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 235244, 1993. [16] P. Pudlak and V. Rodl. Pseudorandom sets and explicit constructions of ramsey graphs. Submitted for publication, 2004. [17] A. Rao. Extractors for a constant number of polynomially small min-entropy independent sources. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing, 2006. [18] R. Raz. Extractors with weak random seeds. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, pages 1120, 2005. [19] O. Reingold, R. Shaltiel, and A. Wigderson. Extracting randomness via repeated condensing. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 2231, 2000. [20] M. Santha and U. V. Vazirani. Generating quasi-random sequences from semi-random sources. Journal of Computer and System Sciences, 33:7587, 1986. [21] R. Shaltiel. Recent developments in explicit constructions of extractors. Bulletin of the European Association for Theoretical Computer Science, 77:6795, 2002. [22] A. Ta-Shma and D. Zuckerman. Extractor codes. IEEE Transactions on Information Theory, 50, 2004. [23] U. Vazirani. Towards a strong communication complexity theory or generating quasi-random sequences from two communicating slightly-random sources (extended abstract). In Proceedings of the 17th Annual ACM Symposium on Theory of Computing, pages 366378, 1985. [24] A. Wigderson and D. Zuckerman. Expanders that beat the eigenvalue bound: Explicit construction and applications. Combinatorica, 19(1):125138, 1999. 680

sum-product theorem;distribution;explicit disperser;construction of disperser;Extractors;recursion;subsource somewhere extractor;structure;bipartite graph;extractors;independent sources;extractor;tools;Ramsey Graphs;disperser;polynomial time computable disperser;resiliency;Theorem;Ramsey graphs;block-sources;deficiency;termination;entropy;Ramsey graph;Independent Sources;algorithms;independent source;subsource;Dispersers;randomness extraction

10

A Frequency-based and a Poisson-based Definition of the Probability of Being Informative

This paper reports on theoretical investigations about the assumptions underlying the inverse document frequency (idf ). We show that an intuitive idf -based probability function for the probability of a term being informative assumes disjoint document events. By assuming documents to be independent rather than disjoint, we arrive at a Poisson-based probability of being informative. The framework is useful for understanding and deciding the parameter estimation and combination in probabilistic retrieval models.

INTRODUCTION AND BACKGROUND The inverse document frequency (idf ) is one of the most successful parameters for a relevance-based ranking of retrieved objects. With N being the total number of documents , and n(t) being the number of documents in which term t occurs, the idf is defined as follows: idf(t) := - log n(t) N , 0 <= idf(t) < Ranking based on the sum of the idf -values of the query terms that occur in the retrieved documents works well, this has been shown in numerous applications. Also, it is well known that the combination of a document-specific term Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SIGIR'03, July 28August 1, 2003, Toronto, Canada. Copyright 2003 ACM 1-58113-646-3/03/0007 ... $ 5.00. weight and idf works better than idf alone. This approach is known as tf-idf , where tf(t, d) (0 <= tf(t, d) <= 1) is the so-called term frequency of term t in document d. The idf reflects the discriminating power (informativeness) of a term, whereas the tf reflects the occurrence of a term. The idf alone works better than the tf alone does. An explanation might be the problem of tf with terms that occur in many documents; let us refer to those terms as "noisy" terms. We use the notion of "noisy" terms rather than "fre-quent" terms since frequent terms leaves open whether we refer to the document frequency of a term in a collection or to the so-called term frequency (also referred to as within-document frequency) of a term in a document. We associate "noise" with the document frequency of a term in a collection, and we associate "occurrence" with the within-document frequency of a term. The tf of a noisy term might be high in a document, but noisy terms are not good candidates for representing a document. Therefore, the removal of noisy terms (known as "stopword removal") is essential when applying tf . In a tf-idf approach, the removal of stopwords is conceptually obsolete, if stopwords are just words with a low idf . From a probabilistic point of view, tf is a value with a frequency-based probabilistic interpretation whereas idf has an "informative" rather than a probabilistic interpretation. The missing probabilistic interpretation of idf is a problem in probabilistic retrieval models where we combine uncertain knowledge of different dimensions (e.g.: informativeness of terms, structure of documents, quality of documents, age of documents, etc.) such that a good estimate of the probability of relevance is achieved. An intuitive solution is a normalisation of idf such that we obtain values in the interval [0; 1]. For example, consider a normalisation based on the maximal idf -value. Let T be the set of terms occurring in a collection. P freq (t is informative) := idf(t) maxidf maxidf := max( {idf(t)|t T }), maxidf <= - log(1/N) minidf := min( {idf(t)|t T }), minidf >= 0 minidf maxidf P freq (t is informative) 1.0 This frequency-based probability function covers the interval [0; 1] if the minimal idf is equal to zero, which is the case if we have at least one term that occurs in all documents. Can we interpret P freq , the normalised idf , as the probability that the term is informative? When investigating the probabilistic interpretation of the 227 normalised idf , we made several observations related to disjointness and independence of document events. These observations are reported in section 3. We show in section 3.1 that the frequency-based noise probability n(t) N used in the classic idf -definition can be explained by three assumptions: binary term occurrence, constant document containment and disjointness of document containment events. In section 3.2 we show that by assuming independence of documents, we obtain 1 - e -1 1 - 0.37 as the upper bound of the noise probability of a term. The value e -1 is related to the logarithm and we investigate in section 3.3 the link to information theory. In section 4, we link the results of the previous sections to probability theory. We show the steps from possible worlds to binomial distribution and Poisson distribution. In section 5, we emphasise that the theoretical framework of this paper is applicable for both idf and tf . Finally, in section 6, we base the definition of the probability of being informative on the results of the previous sections and compare frequency-based and Poisson-based definitions. BACKGROUND The relationship between frequencies, probabilities and information theory (entropy) has been the focus of many researchers. In this background section, we focus on work that investigates the application of the Poisson distribution in IR since a main part of the work presented in this paper addresses the underlying assumptions of Poisson. [4] proposes a 2-Poisson model that takes into account the different nature of relevant and non-relevant documents, rare terms (content words) and frequent terms (noisy terms, function words, stopwords). [9] shows experimentally that most of the terms (words) in a collection are distributed according to a low dimension n-Poisson model. [10] uses a 2-Poisson model for including term frequency-based probabilities in the probabilistic retrieval model. The non-linear scaling of the Poisson function showed significant improvement compared to a linear frequency-based probability. The Poisson model was here applied to the term frequency of a term in a document. We will generalise the discussion by pointing out that document frequency and term frequency are dual parameters in the collection space and the document space, respectively. Our discussion of the Poisson distribution focuses on the document frequency in a collection rather than on the term frequency in a document. [7] and [6] address the deviation of idf and Poisson, and apply Poisson mixtures to achieve better Poisson-based estimates . The results proved again experimentally that a one-dimensional Poisson does not work for rare terms, therefore Poisson mixtures and additional parameters are proposed. [3], section 3.3, illustrates and summarises comprehen-sively the relationships between frequencies, probabilities and Poisson. Different definitions of idf are put into context and a notion of "noise" is defined, where noise is viewed as the complement of idf . We use in our paper a different notion of noise: we consider a frequency-based noise that corresponds to the document frequency, and we consider a term noise that is based on the independence of document events. [11], [12], [8] and [1] link frequencies and probability estimation to information theory. [12] establishes a framework in which information retrieval models are formalised based on probabilistic inference. A key component is the use of a space of disjoint events, where the framework mainly uses terms as disjoint events. The probability of being informative defined in our paper can be viewed as the probability of the disjoint terms in the term space of [12]. [8] address entropy and bibliometric distributions. Entropy is maximal if all events are equiprobable and the frequency -based Lotka law (N/i is the number of scientists that have written i publications, where N and are distribution parameters), Zipf and the Pareto distribution are related . The Pareto distribution is the continuous case of the Lotka and Lotka and Zipf show equivalences. The Pareto distribution is used by [2] for term frequency normalisation. The Pareto distribution compares to the Poisson distribution in the sense that Pareto is "fat-tailed", i. e. Pareto assigns larger probabilities to large numbers of events than Poisson distributions do. This makes Pareto interesting since Poisson is felt to be too radical on frequent events. We restrict in this paper to the discussion of Poisson, however , our results show that indeed a smoother distribution than Poisson promises to be a good candidate for improving the estimation of probabilities in information retrieval. [1] establishes a theoretical link between tf-idf and information theory and the theoretical research on the meaning of tf-idf "clarifies the statistical model on which the different measures are commonly based". This motivation matches the motivation of our paper: We investigate theoretically the assumptions of classical idf and Poisson for a better understanding of parameter estimation and combination. FROM DISJOINT TO INDEPENDENT We define and discuss in this section three probabilities: The frequency-based noise probability (definition 1), the total noise probability for disjoint documents (definition 2). and the noise probability for independent documents (definition 3). 3.1 Binary occurrence, constant containment and disjointness of documents We show in this section, that the frequency-based noise probability n(t) N in the idf definition can be explained as a total probability with binary term occurrence, constant document containment and disjointness of document containments . We refer to a probability function as binary if for all events the probability is either 1.0 or 0.0. The occurrence probability P (t|d) is binary, if P (t|d) is equal to 1.0 if t d, and P (t|d) is equal to 0.0, otherwise. P (t|d) is binary : P (t|d) = 1.0 P (t|d) = 0.0 We refer to a probability function as constant if for all events the probability is equal. The document containment probability reflect the chance that a document occurs in a collection. This containment probability is constant if we have no information about the document containment or we ignore that documents differ in containment. Containment could be derived, for example, from the size, quality, age, links, etc. of a document. For a constant containment in a collection with N documents, 1 N is often assumed as the containment probability. We generalise this definition and introduce the constant where 0 N. The containment of a document d depends on the collection c, this is reflected by the notation P (d|c) used for the containment 228 of a document. P (d|c) is constant : d : P (d|c) = N For disjoint documents that cover the whole event space, we set = 1 and obtain d P (d|c) = 1.0. Next, we define the frequency-based noise probability and the total noise probability for disjoint documents. We introduce the event notation t is noisy and t occurs for making the difference between the noise probability P (t is noisy|c) in a collection and the occurrence probability P (t occurs|d) in a document more explicit, thereby keeping in mind that the noise probability corresponds to the occurrence probability of a term in a collection. Definition 1. The frequency-based term noise probability : P freq (t is noisy|c) := n(t) N Definition 2. The total term noise probability for disjoint documents: P dis (t is noisy|c) := d P (t occurs|d) P (d|c) Now, we can formulate a theorem that makes assumptions explicit that explain the classical idf . Theorem 1. IDF assumptions: If the occurrence probability P (t|d) of term t over documents d is binary, and the containment probability P (d|c) of documents d is constant , and document containments are disjoint events, then the noise probability for disjoint documents is equal to the frequency-based noise probability. P dis (t is noisy|c) = P freq (t is noisy|c) Proof. The assumptions are: d : (P (t occurs|d) = 1 P (t occurs|d) = 0) P (d|c) = N d P (d|c) = 1.0 We obtain: P dis (t is noisy|c) = d|td 1 N = n(t) N = P freq (t is noisy|c) The above result is not a surprise but it is a mathematical formulation of assumptions that can be used to explain the classical idf . The assumptions make explicit that the different types of term occurrence in documents (frequency of a term, importance of a term, position of a term, document part where the term occurs, etc.) and the different types of document containment (size, quality, age, etc.) are ignored, and document containments are considered as disjoint events. From the assumptions, we can conclude that idf (frequency-based noise, respectively) is a relatively simple but strict estimate. Still, idf works well. This could be explained by a leverage effect that justifies the binary occurrence and constant containment: The term occurrence for small documents tends to be larger than for large documents, whereas the containment for small documents tends to be smaller than for large documents. From that point of view, idf means that P (t d|c) is constant for all d in which t occurs, and P (t d|c) is zero otherwise. The occurrence and containment can be term specific. For example, set P (t d|c) = 1/N D (c) if t occurs in d, where N D (c) is the number of documents in collection c (we used before just N). We choose a document-dependent occurrence P (t|d) := 1/N T (d), i. e. the occurrence probability is equal to the inverse of N T (d), which is the total number of terms in document d. Next, we choose the containment P (d|c) := N T (d)/N T (c)N T (c)/N D (c) where N T (d)/N T (c) is a document length normalisation (number of terms in document d divided by the number of terms in collection c), and N T (c)/N D (c) is a constant factor of the collection (number of terms in collection c divided by the number of documents in collection c). We obtain P (td|c) = 1/N D (c). In a tf-idf -retrieval function, the tf -component reflects the occurrence probability of a term in a document. This is a further explanation why we can estimate the idf with a simple P (t|d), since the combined tf-idf contains the occurrence probability. The containment probability corresponds to a document normalisation (document length normalisation , pivoted document length) and is normally attached to the tf -component or the tf-idf -product. The disjointness assumption is typical for frequency-based probabilities. From a probability theory point of view, we can consider documents as disjoint events, in order to achieve a sound theoretical model for explaining the classical idf . But does disjointness reflect the real world where the containment of a document appears to be independent of the containment of another document? In the next section, we replace the disjointness assumption by the independence assumption . 3.2 The upper bound of the noise probability for independent documents For independent documents, we compute the probability of a disjunction as usual, namely as the complement of the probability of the conjunction of the negated events: P (d 1 . . . d N ) = 1 - P (d 1 . . . d N ) = 1 d (1 - P (d)) The noise probability can be considered as the conjunction of the term occurrence and the document containment. P (t is noisy|c) := P (t occurs (d 1 . . . d N ) |c) For disjoint documents, this view of the noise probability led to definition 2. For independent documents, we use now the conjunction of negated events. Definition 3. The term noise probability for independent documents: P in (t is noisy|c) := d (1 - P (t occurs|d) P (d|c)) With binary occurrence and a constant containment P (d|c) := /N, we obtain the term noise of a term t that occurs in n(t) documents: P in (t is noisy|c) = 1 - 1 N n(t) 229 For binary occurrence and disjoint documents, the containment probability was 1/N. Now, with independent documents , we can use as a collection parameter that controls the average containment probability. We show through the next theorem that the upper bound of the noise probability depends on . Theorem 2. The upper bound of being noisy: If the occurrence P (t|d) is binary, and the containment P (d|c) is constant, and document containments are independent events, then 1 - e is the upper bound of the noise probability . t : P in (t is noisy|c) < 1 - e Proof . The upper bound of the independent noise probability follows from the limit lim N (1 + x N ) N = e x (see any comprehensive math book, for example, [5], for the convergence equation of the Euler function). With x = -, we obtain: lim N 1 N N = e For the term noise, we have: P in (t is noisy|c) = 1 - 1 N n(t) P in (t is noisy|c) is strictly monotonous: The noise of a term t n is less than the noise of a term t n+1 , where t n occurs in n documents and t n+1 occurs in n + 1 documents. Therefore , a term with n = N has the largest noise probability. For a collection with infinite many documents, the upper bound of the noise probability for terms t N that occur in all documents becomes: lim N P in (t N is noisy) = lim N 1 - 1 N N = 1 - e By applying an independence rather a disjointness assumption , we obtain the probability e -1 that a term is not noisy even if the term does occur in all documents. In the disjoint case, the noise probability is one for a term that occurs in all documents. If we view P (d|c) := /N as the average containment, then is large for a term that occurs mostly in large documents , and is small for a term that occurs mostly in small documents. Thus, the noise of a term t is large if t occurs in n(t) large documents and the noise is smaller if t occurs in small documents. Alternatively, we can assume a constant containment and a term-dependent occurrence. If we assume P (d|c) := 1, then P (t|d) := /N can be interpreted as the average probability that t represents a document. The common assumption is that the average containment or occurrence probability is proportional to n(t). However, here is additional potential: The statistical laws (see [3] on Luhn and Zipf) indicate that the average probability could follow a normal distribution, i. e. small probabilities for small n(t) and large n(t), and larger probabilities for medium n(t). For the monotonous case we investigate here, the noise of a term with n(t) = 1 is equal to 1 - (1 - /N) = /N and the noise of a term with n(t) = N is close to 1 - e . In the next section, we relate the value e to information theory. 3.3 The probability of a maximal informative signal The probability e -1 is special in the sense that a signal with that probability is a signal with maximal information as derived from the entropy definition. Consider the definition of the entropy contribution H(t) of a signal t. H(t) := P (t) - ln P (t) We form the first derivation for computing the optimum. H(t) P (t) = - ln P (t) + -1 P (t) P (t) = -(1 + ln P (t)) For obtaining optima, we use: 0 = -(1 + ln P (t)) The entropy contribution H(t) is maximal for P (t) = e -1 . This result does not depend on the base of the logarithm as we see next: H(t) P (t) = - log b P (t) + -1 P (t) ln b P (t) = 1 ln b + log b P (t) = 1 + ln P (t) ln b We summarise this result in the following theorem: Theorem 3. The probability of a maximal informative signal: The probability P max = e -1 0.37 is the probability of a maximal informative signal. The entropy of a maximal informative signal is H max = e -1 . Proof. The probability and entropy follow from the derivation above. The complement of the maximal noise probability is e and we are looking now for a generalisation of the entropy definition such that e is the probability of a maximal informative signal. We can generalise the entropy definition by computing the integral of + ln P (t), i. e. this derivation is zero for e . We obtain a generalised entropy: -( + ln P (t)) d(P (t)) = P (t) (1 - - ln P (t)) The generalised entropy corresponds for = 1 to the classical entropy. By moving from disjoint to independent documents , we have established a link between the complement of the noise probability of a term that occurs in all documents and information theory. Next, we link independent documents to probability theory. THE LINK TO PROBABILITY THEORY We review for independent documents three concepts of probability theory: possible worlds, binomial distribution and Poisson distribution. 4.1 Possible Worlds Each conjunction of document events (for each document, we consider two document events: the document can be true or false) is associated with a so-called possible world. For example, consider the eight possible worlds for three documents (N = 3). 230 world w conjunction w 7 d 1 d 2 d 3 w 6 d 1 d 2 d 3 w 5 d 1 d 2 d 3 w 4 d 1 d 2 d 3 w 3 d 1 d 2 d 3 w 2 d 1 d 2 d 3 w 1 d 1 d 2 d 3 w 0 d 1 d 2 d 3 With each world w, we associate a probability (w), which is equal to the product of the single probabilities of the document events. world w probability (w) w 7 N 3 1 N 0 w 6 N 2 1 N 1 w 5 N 2 1 N 1 w 4 N 1 1 N 2 w 3 N 2 1 N 1 w 2 N 1 1 N 2 w 1 N 1 1 N 2 w 0 N 0 1 N 3 The sum over the possible worlds in which k documents are true and N -k documents are false is equal to the probability function of the binomial distribution, since the binomial coefficient yields the number of possible worlds in which k documents are true. 4.2 Binomial distribution The binomial probability function yields the probability that k of N events are true where each event is true with the single event probability p. P (k) := binom(N, k, p) := N k p k (1 - p)N -k The single event probability is usually defined as p := /N, i. e. p is inversely proportional to N, the total number of events. With this definition of p, we obtain for an infinite number of documents the following limit for the product of the binomial coefficient and p k : lim N N k p k = = lim N N (N -1) . . . (N -k +1) k! N k = k k! The limit is close to the actual value for k << N. For large k, the actual value is smaller than the limit. The limit of (1 -p)N -k follows from the limit lim N (1+ x N ) N = e x . lim N (1 - p) N-k = lim N 1 N N -k = lim N e 1 N -k = e Again , the limit is close to the actual value for k << N. For large k, the actual value is larger than the limit. 4.3 Poisson distribution For an infinite number of events, the Poisson probability function is the limit of the binomial probability function. lim N binom(N, k, p) = k k! e P (k) = poisson(k, ) := k k! e The probability poisson (0, 1) is equal to e -1 , which is the probability of a maximal informative signal. This shows the relationship of the Poisson distribution and information theory. After seeing the convergence of the binomial distribution, we can choose the Poisson distribution as an approximation of the independent term noise probability. First, we define the Poisson noise probability: Definition 4. The Poisson term noise probability: P poi (t is noisy|c) := e n(t) k=1 k k! For independent documents, the Poisson distribution approximates the probability of the disjunction for large n(t), since the independent term noise probability is equal to the sum over the binomial probabilities where at least one of n(t) document containment events is true. P in (t is noisy|c) = n(t) k=1 n(t) k p k (1 - p)N -k P in (t is noisy|c) P poi (t is noisy|c) We have defined a frequency-based and a Poisson-based probability of being noisy, where the latter is the limit of the independence-based probability of being noisy. Before we present in the final section the usage of the noise probability for defining the probability of being informative, we emphasise in the next section that the results apply to the collection space as well as to the the document space. THE COLLECTION SPACE AND THE DOCUMENT SPACE Consider the dual definitions of retrieval parameters in table 1. We associate a collection space D T with a collection c where D is the set of documents and T is the set of terms in the collection. Let N D := |D| and N T := |T | be the number of documents and terms, respectively. We consider a document as a subset of T and a term as a subset of D. Let n T (d) := |{t|d t}| be the number of terms that occur in the document d, and let n D (t) := |{d|t d}| be the number of documents that contain the term t. In a dual way, we associate a document space L T with a document d where L is the set of locations (also referred to as positions, however, we use the letters L and l and not P and p for avoiding confusion with probabilities) and T is the set of terms in the document. The document dimension in a collection space corresponds to the location (position) dimension in a document space. The definition makes explicit that the classical notion of term frequency of a term in a document (also referred to as the within-document term frequency) actually corresponds to the location frequency of a term in a document. For the 231 space collection document dimensions documents and terms locations and terms document/location frequency n D (t, c): Number of documents in which term t occurs in collection c n L (t, d): Number of locations (positions) at which term t occurs in document d N D (c): Number of documents in collection c N L (d): Number of locations (positions) in document d term frequency n T (d, c): Number of terms that document d contains in collection c n T (l, d): Number of terms that location l contains in document d N T (c): Number of terms in collection c N T (d): Number of terms in document d noise/occurrence P (t|c) (term noise) P (t|d) (term occurrence) containment P (d|c) (document) P (l|d) (location) informativeness - ln P (t|c) - ln P (t|d) conciseness - ln P (d|c) - ln P (l|d) P(informative) ln(P (t|c))/ ln(P (t min , c)) ln(P (t|d))/ ln(P (t min , d)) P(concise) ln(P (d|c))/ ln(P (d min |c)) ln(P (l|d))/ ln(P (l min |d)) Table 1: Retrieval parameters actual term frequency value, it is common to use the maximal occurrence (number of locations; let lf be the location frequency). tf(t, d) := lf(t, d) := P freq (t occurs|d) P freq (t max occurs |d) = n L (t, d) n L (t max , d) A further duality is between informativeness and conciseness (shortness of documents or locations): informativeness is based on occurrence (noise), conciseness is based on containment . We have highlighted in this section the duality between the collection space and the document space. We concentrate in this paper on the probability of a term to be noisy and informative. Those probabilities are defined in the collection space. However, the results regarding the term noise and informativeness apply to their dual counterparts: term occurrence and informativeness in a document. Also, the results can be applied to containment of documents and locations THE PROBABILITY OF BEING INFORMATIVE We showed in the previous sections that the disjointness assumption leads to frequency-based probabilities and that the independence assumption leads to Poisson probabilities. In this section, we formulate a frequency-based definition and a Poisson-based definition of the probability of being informative and then we compare the two definitions. Definition 5. The frequency-based probability of being informative: P freq (t is informative|c) := - ln n(t) N - ln 1 N = - log N n(t) N = 1 - log N n(t) = 1 - ln n(t) ln N We define the Poisson-based probability of being informative analogously to the frequency-based probability of being informative (see definition 5). Definition 6. The Poisson-based probability of being informative: P poi (t is informative|c) := ln e n(t) k=1 k k! - ln(e ) = - ln n(t) k=1 k k! - ln For the sum expression, the following limit holds: lim n(t) n(t) k=1 k k! = e - 1 For >> 1, we can alter the noise and informativeness Poisson by starting the sum from 0, since e >> 1. Then, the minimal Poisson informativeness is poisson(0, ) = e . We obtain a simplified Poisson probability of being informative: P poi (t is informative|c) - ln n(t) k=0 k k! = 1 - ln n(t) k=0 k k! The computation of the Poisson sum requires an optimi-sation for large n(t). The implementation for this paper exploits the nature of the Poisson density: The Poisson density yields only values significantly greater than zero in an interval around . Consider the illustration of the noise and informativeness definitions in figure 1. The probability functions displayed are summarised in figure 2 where the simplified Poisson is used in the noise and informativeness graphs. The frequency-based noise corresponds to the linear solid curve in the noise figure. With an independence assumption, we obtain the curve in the lower triangle of the noise figure. By changing the parameter p := /N of the independence probability , we can lift or lower the independence curve. The noise figure shows the lifting for the value := ln N 9.2. The setting = ln N is special in the sense that the frequency-based and the Poisson-based informativeness have the same denominator, namely ln N, and the Poisson sum converges to . Whether we can draw more conclusions from this setting is an open question. We can conclude, that the lifting is desirable if we know for a collection that terms that occur in relatively few doc-232 0 0.2 0.4 0.6 0.8 1 0 2000 4000 6000 8000 10000 Probability of being noisy n(t): Number of documents with term t frequency independence: 1/N independence: ln(N)/N poisson: 1000 poisson: 2000 poisson: 1000,2000 0 0.2 0.4 0.6 0.8 1 0 2000 4000 6000 8000 10000 Probability of being informative n(t): Number of documents with term t frequency independence: 1/N independence: ln(N)/N poisson: 1000 poisson: 2000 poisson: 1000,2000 Figure 1: Noise and Informativeness Probability function Noise Informativeness Frequency P freq Def n(t)/N ln(n(t)/N)/ ln(1/N) Interval 1/N P freq 1.0 0.0 P freq 1.0 Independence P in Def 1 - (1 - p) n(t) ln(1 - (1 - p) n(t) )/ ln(p) Interval p P in < 1 - e ln (p) P in 1.0 Poisson P poi Def e n(t) k=1 k k! ( - ln n(t) k=1 k k! )/( - ln ) Interval e P poi < 1 - e ( - ln(e - 1))/( - ln ) P poi 1.0 Poisson P poi simplified Def e n(t) k=0 k k! ( - ln n(t) k=0 k k! )/ Interval e P poi < 1.0 0.0 < P poi 1.0 Figure 2: Probability functions uments are no guarantee for finding relevant documents, i. e. we assume that rare terms are still relatively noisy. On the opposite, we could lower the curve when assuming that frequent terms are not too noisy, i. e. they are considered as being still significantly discriminative. The Poisson probabilities approximate the independence probabilities for large n(t); the approximation is better for larger . For n(t) < , the noise is zero whereas for n(t) > the noise is one. This radical behaviour can be smoothened by using a multi-dimensional Poisson distribution. Figure 1 shows a Poisson noise based on a two-dimensional Poisson: poisson(k, 1 , 2 ) := e 1 k 1 k! + (1 - ) e 2 k 2 k! The two dimensional Poisson shows a plateau between 1 = 1000 and 2 = 2000, we used here = 0.5. The idea behind this setting is that terms that occur in less than 1000 documents are considered to be not noisy (i.e. they are informative ), that terms between 1000 and 2000 are half noisy, and that terms with more than 2000 are definitely noisy. For the informativeness, we observe that the radical behaviour of Poisson is preserved. The plateau here is approximately at 1/6, and it is important to realise that this plateau is not obtained with the multi-dimensional Poisson noise using = 0.5. The logarithm of the noise is normalised by the logarithm of a very small number, namely 0.5 e -1000 + 0.5 e -2000 . That is why the informativeness will be only close to one for very little noise, whereas for a bit of noise, informativeness will drop to zero. This effect can be controlled by using small values for such that the noise in the interval [ 1 ; 2 ] is still very little. The setting = e -2000/6 leads to noise values of approximately e -2000/6 in the interval [ 1 ; 2 ], the logarithms lead then to 1/6 for the informativeness. The indepence-based and frequency-based informativeness functions do not differ as much as the noise functions do. However, for the indepence-based probability of being informative , we can control the average informativeness by the definition p := /N whereas the control on the frequency-based is limited as we address next. For the frequency-based idf , the gradient is monotonously decreasing and we obtain for different collections the same distances of idf -values, i. e. the parameter N does not affect the distance. For an illustration, consider the distance between the value idf(t n+1 ) of a term t n+1 that occurs in n+1 documents, and the value idf(t n ) of a term t n that occurs in n documents. idf(t n+1 ) - idf(t n ) = ln n n + 1 The first three values of the distance function are: idf(t 2 ) - idf(t 1 ) = ln(1/(1 + 1)) = 0.69 idf(t 3 ) - idf(t 2 ) = ln(1/(2 + 1)) = 0.41 idf(t 4 ) - idf(t 3 ) = ln(1/(3 + 1)) = 0.29 For the Poisson-based informativeness, the gradient decreases first slowly for small n(t), then rapidly near n(t) and then it grows again slowly for large n(t). In conclusion, we have seen that the Poisson-based definition provides more control and parameter possibilities than 233 the frequency-based definition does. Whereas more control and parameter promises to be positive for the personalisa-tion of retrieval systems, it bears at the same time the danger of just too many parameters. The framework presented in this paper raises the awareness about the probabilistic and information-theoretic meanings of the parameters. The parallel definitions of the frequency-based probability and the Poisson-based probability of being informative made the underlying assumptions explicit. The frequency-based probability can be explained by binary occurrence, constant containment and disjointness of documents. Independence of documents leads to Poisson, where we have to be aware that Poisson approximates the probability of a disjunction for a large number of events, but not for a small number. This theoretical result explains why experimental investigations on Poisson (see [7]) show that a Poisson estimation does work better for frequent (bad, noisy) terms than for rare (good, informative) terms. In addition to the collection-wide parameter setting, the framework presented here allows for document-dependent settings, as explained for the independence probability. This is in particular interesting for heterogeneous and structured collections, since documents are different in nature (size, quality, root document, sub document), and therefore, binary occurrence and constant containment are less appropriate than in relatively homogeneous collections. SUMMARY The definition of the probability of being informative transforms the informative interpretation of the idf into a probabilistic interpretation, and we can use the idf -based probability in probabilistic retrieval approaches. We showed that the classical definition of the noise (document frequency) in the inverse document frequency can be explained by three assumptions: the term within-document occurrence probability is binary, the document containment probability is constant, and the document containment events are disjoint. By explicitly and mathematically formulating the assumptions , we showed that the classical definition of idf does not take into account parameters such as the different nature (size, quality, structure, etc.) of documents in a collection, or the different nature of terms (coverage, importance, position , etc.) in a document. We discussed that the absence of those parameters is compensated by a leverage effect of the within-document term occurrence probability and the document containment probability. By applying an independence rather a disjointness assumption for the document containment, we could establish a link between the noise probability (term occurrence in a collection), information theory and Poisson. From the frequency-based and the Poisson-based probabilities of being noisy, we derived the frequency-based and Poisson-based probabilities of being informative. The frequency-based probability is relatively smooth whereas the Poisson probability is radical in distinguishing between noisy or not noisy, and informative or not informative, respectively. We showed how to smoothen the radical behaviour of Poisson with a multi-dimensional Poisson. The explicit and mathematical formulation of idf - and Poisson-assumptions is the main result of this paper. Also, the paper emphasises the duality of idf and tf , collection space and document space, respectively. Thus, the result applies to term occurrence and document containment in a collection, and it applies to term occurrence and position containment in a document. This theoretical framework is useful for understanding and deciding the parameter estimation and combination in probabilistic retrieval models. The links between indepence-based noise as document frequency, probabilistic interpretation of idf , information theory and Poisson described in this paper may lead to variable probabilistic idf and tf definitions and combinations as required in advanced and personalised information retrieval systems. Acknowledgment: I would like to thank Mounia Lalmas, Gabriella Kazai and Theodora Tsikrika for their comments on the as they said "heavy" pieces. My thanks also go to the meta-reviewer who advised me to improve the presentation to make it less "formidable" and more accessible for those "without a theoretic bent". This work was funded by a research fellowship from Queen Mary University of London. REFERENCES [1] A. Aizawa. An information-theoretic perspective of tf-idf measures. Information Processing and Management, 39:4565, January 2003. [2] G. Amati and C. J. Rijsbergen. Term frequency normalization via Pareto distributions. In 24th BCS-IRSG European Colloquium on IR Research, Glasgow, Scotland, 2002. [3] R. K. Belew. Finding out about. Cambridge University Press, 2000. [4] A. Bookstein and D. Swanson. Probabilistic models for automatic indexing. Journal of the American Society for Information Science, 25:312318, 1974. [5] I. N. Bronstein. Taschenbuch der Mathematik. Harri Deutsch, Thun, Frankfurt am Main, 1987. [6] K. Church and W. Gale. Poisson mixtures. Natural Language Engineering, 1(2):163190, 1995. [7] K. W. Church and W. A. Gale. Inverse document frequency: A measure of deviations from poisson. In Third Workshop on Very Large Corpora, ACL Anthology, 1995. [8] T. Lafouge and C. Michel. Links between information construction and information gain: Entropy and bibliometric distribution. Journal of Information Science, 27(1):3949, 2001. [9] E. Margulis. N-poisson document modelling. In Proceedings of the 15th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 177189, 1992. [10] S. E. Robertson and S. Walker. Some simple effective approximations to the 2-poisson model for probabilistic weighted retrieval. In Proceedings of the 17th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 232241, London, et al., 1994. Springer-Verlag. [11] S. Wong and Y. Yao. An information-theoric measure of term specificity. Journal of the American Society for Information Science, 43(1):5461, 1992. [12] S. Wong and Y. Yao. On modeling information retrieval with probabilistic inference. ACM Transactions on Information Systems, 13(1):3868, 1995. 234

inverse document frequency (idf);independent and disjoint documents;computer science;information search;probability theories;Poisson based probability;Term frequency;probabilistic retrieval models;Probability of being informative;Independent documents;Disjoint documents;Normalisation;relevance-based ranking of retrieved objects;information theory;Noise probability;frequency-based term noise probability;Poisson-based probability of being informative;Assumptions;Collection space;Poisson distribution;Probabilistic information retrieval;Document space;document retrieval;entropy;Frequency-based probability;Document frequency;Inverse document frequency;Information theory;independence assumption;inverse document frequency;maximal informative signal

100

High Performance Crawling System

In the present paper, we will describe the design and implementation of a real-time distributed system of Web crawling running on a cluster of machines. The system crawls several thousands of pages every second, includes a high-performance fault manager, is platform independent and is able to adapt transparently to a wide range of configurations without incurring additional hardware expenditure. We will then provide details of the system architecture and describe the technical choices for very high performance crawling. Finally, we will discuss the experimental results obtained, comparing them with other documented systems.

INTRODUCTION With the World Wide Web containing the vast amount of information (several thousands in 1993, 3 billion today) that it does and the fact that it is ever expanding, we need a way to find the right information (multimedia of textual). We need a way to access the information on specific subjects that we require. To solve the problems above several programs and algorithms were designed that index the web, these various designs are known as search engines, spiders, crawlers, worms or knowledge robots graph in its simplest terms. The pages are the nodes on the graph and the links are the arcs on the graph. What makes this so difficult is the vast amount of data that we have to handle, and then we must also take into account the fact that the World Wide Web is constantly growing and the fact that people are constantly updating the content of their web pages. Any High performance crawling system should offer at least the following two features. Firstly, it needs to be equipped with an intelligent navigation strategy, i.e. enabling it to make decisions regarding the choice of subsequent actions to be taken (pages to be downloaded etc). Secondly, its supporting hardware and software architecture should be optimized to crawl large quantities of documents per unit of time (generally per second). To this we may add fault tolerance (machine crash, network failure etc.) and considerations of Web server resources. Recently we have seen a small interest in these two field. Studies on the first point include crawling strategies for important pages [9, 17], topic-specific document downloading [5, 6, 18, 10], page recrawling to optimize overall refresh frequency of a Web archive [8, 7] or scheduling the downloading activity according to time [22]. However, little research has been devoted to the second point, being very difficult to implement [20, 13]. We will focus on this latter point in the rest of this paper. Indeed, only a few crawlers are equipped with an optimized scalable crawling system, yet details of their internal workings often remain obscure (the majority being proprietary solutions). The only system to have been given a fairly in-depth description in existing literature is Mercator by Heydon and Najork of DEC/Compaq [13] used in the AltaVista search engine (some details also exist on the first version of the Google [3] and Internet Archive [4] robots). Most recent studies on crawling strategy fail to deal with these features, contenting themselves with the solution of minor issues such as the calculation of the number of pages to be downloaded in order to maximize/minimize some functional objective. This may be acceptable in the case of small applications, but for real time 1 applications the system must deal with a much larger number of constraints. We should also point out that little academic research is concerned with high performance search engines, as compared with their commercial counterparts (with the exception of the WebBase project [14] at Stanford). In the present paper, we will describe a very high availability, optimized and distributed crawling system. We will use the system on what is known as breadth-first crawling, though this may be easily adapted to other navigation strategies. We will first focus on input/output, on management of network traffic and robustness when changing scale. We will also discuss download policies in 1 "Soft" real time 299 Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. MIR'04, October 1516, 2004, New York, New York, USA. Copyright 2004 ACM 1-58113-940-3/04/0010...$5.00. terms of speed regulation, fault management by supervisors and the introduction/suppression of machine nodes without system restart during a crawl. Our system was designed within the experimental framework of the D ep^ ot L egal du Web Fran cais (French Web Legal Deposit). This consists of archiving only multimedia documents in French available on line, indexing them and providing ways for these archives to be consulted. Legal deposit requires a real crawling strategy in order to ensure site continuity over time. The notion of registration is closely linked to that of archiving, which requires a suitable strategy to be useful. In the course of our discussion, we will therefore analyze the implication and impact of this experimentation for system construction. STATE OF THE ART In order to set our work in this field in context, listed below are definitions of services that should be considered the minimum requirements for any large-scale crawling system. Flexibility: as mentioned above, with some minor adjustments our system should be suitable for various scenarios. However, it is important to remember that crawling is established within a specific framework: namely, Web legal deposit. High Performance: the system needs to be scalable with a minimum of one thousand pages/second and extending up to millions of pages for each run on low cost hardware. Note that here, the quality and efficiency of disk access are crucial to maintaining high performance. Fault Tolerance: this may cover various aspects. As the system interacts with several servers at once, specific problems emerge. First, it should at least be able to process invalid HTML code, deal with unexpected Web server behavior, and select good communication protocols etc. The goal here is to avoid this type of problem and, by force of circumstance, to be able to ignore such problems completely. Second, crawling processes may take days or weeks, and it is imperative that the system can handle failure, stopped processes or interruptions in network services, keeping data loss to a minimum. Finally, the system should be persistent, which means periodically switching large data structures from memory to the disk (e.g. restart after failure). Maintainability and Configurability: an appropriate interface is necessary for monitoring the crawling process, including download speed, statistics on the pages and amounts of data stored. In online mode, the administrator may adjust the speed of a given crawler, add or delete processes, stop the system, add or delete system nodes and supply the black list of domains not to be visited, etc. 2.2 General Crawling Strategies There are many highly accomplished techniques in terms of Web crawling strategy. We will describe the most relevant of these here. Breadth-first Crawling: in order to build a wide Web archive like that of the Internet Archive [15], a crawl is carried out from a set of Web pages (initial URLs or seeds). A breadth-first exploration is launched by following hypertext links leading to those pages directly connected with this initial set. In fact, Web sites are not really browsed breadth-first and various restrictions may apply, e.g. limiting crawling processes to within a site, or downloading the pages deemed most interesting first 2 Repetitive Crawling: once pages have been crawled, some systems require the process to be repeated periodically so that indexes are kept updated. In the most basic case, this may be achieved by launching a second crawl in parallel. A variety of heuristics exist to overcome this problem: for example, by frequently relaunching the crawling process of pages, sites or domains considered important to the detriment of others. A good crawling strategy is crucial for maintaining a constantly updated index list. Recent studies by Cho and Garcia-Molina [8, 7] have focused on optimizing the update frequency of crawls by using the history of changes recorded on each site. Targeted Crawling: more specialized search engines use crawling process heuristics in order to target a certain type of page, e.g. pages on a specific topic or in a particular language, images, mp3 files or scientific papers. In addition to these heuristics, more generic approaches have been suggested. They are based on the analysis of the structures of hypertext links [6, 5] and techniques of learning [9, 18]: the objective here being to retrieve the greatest number of pages relating to a particular subject by using the minimum bandwidth. Most of the studies cited in this category do not use high performance crawlers, yet succeed in producing acceptable results. Random Walks and Sampling: some studies have focused on the effect of random walks on Web graphs or modified versions of these graphs via sampling in order to estimate the size of documents on line [1, 12, 11]. Deep Web Crawling: a lot of data accessible via the Web are currently contained in databases and may only be downloaded through the medium of appropriate requests or forms. Recently, this often-neglected but fascinating problem has been the focus of new interest. The Deep Web is the name given to the Web containing this category of data [9]. Lastly, we should point out the acknowledged differences that exist between these scenarios. For example, a breadth-first search needs to keep track of all pages already crawled. An analysis of links should use structures of additional data to represent the graph of the sites in question, and a system of classifiers in order to assess the pages' relevancy [6, 5]. However, some tasks are common to all scenarios, such as 2 See [9] for the heuristics that tend to find the most important pages first and [17] for experimental results proving that breadth-first crawling allows the swift retrieval of pages with a high PageRank. 300 respecting robot exclusion files (robots.txt), crawling speed, resolution of domain names . . . In the early 1990s, several companies claimed that their search engines were able to provide complete Web coverage. It is now clear that only partial coverage is possible at present. Lawrence and Giles [16] carried out two experiments in order to measure coverage performance of data established by crawlers and of their updates. They adopted an approach known as overlap analysis to estimate the size of the Web that may be indexed (See also Bharat and Broder 1998 on the same subject). Let W be the total set of Web pages and W a W and W b W the pages downloaded by two different crawlers a and b. What is the size of W a and W b as compared with W ? Let us assume that uniform samples of Web pages may be taken and their membership of both sets tested. Let P (W a ) and P (W b ) be the probability that a page is downloaded by a or b respectively. We know that: P (W a W b |W b ) = W a W b |W b | (1) Now, if these two crawling processes are assumed to be independent, the left side of equation 1may be reduced to P (W a ), that is data coverage by crawler a. This may be easily obtained by the intersection size of the two crawling processes. However, an exact calculation of this quantity is only possible if we do not really know the documents crawled. Lawrence and Giles used a set of controlled data of 575 requests to provide page samples and count the number of times that the two crawlers retrieved the same pages. By taking the hypothesis that the result P (W a ) is correct, we may estimate the size of the Web as |W a |/P (W a ). This approach has shown that the Web contained at least 320 million pages in 1997 and that only 60% was covered by the six major search engines of that time. It is also interesting to note that a single search engine would have covered only 1/3 of the Web. As this approach is based on observation, it may reflect a visible Web estimation, excluding for instance pages behind forms, databases etc. More recent experiments assert that the Web contains several billion pages. 2.2.1 Selective Crawling As demonstrated above, a single crawler cannot archive the whole Web. The fact is that the time required to carry out the complete crawling process is very long, and impossible given the technology currently available. Furthermore, crawling and indexing very large amounts of data implies great problems of scalability, and consequently entails not inconsiderable costs of hardware and maintenance. For maximum optimization, a crawling system should be able to recognize relevant sites and pages, and restrict itself to downloading within a limited time. A document or Web page's relevancy may be officially recognized in various ways. The idea of selective crawling may be introduced intuitively by associating each URL u with a score calculation function s () respecting relevancy criterion and parameters . In the most basic case, we may assume a Boolean relevancy function, i.e. s(u) = 1 if the document designated by u is relevant and s(u) = 0 if not. More generally, we may think of s(d) as a function with real values, such as a conditional probability that a document belongs to a certain category according to its content. In all cases, we should point out that the score calculation function depends only on the URL and and not on the time or state of the crawler. A general approach for the construction of a selective crawler consists of changing the URL insertion and extraction policy in the queue Q of the crawler. Let us assume that the URLs are sorted in the order corresponding to the value retrieved by s(u). In this case, we obtain the best-first strategy (see [19]) which consists of downloading URLs with the best scores first). If s(u) provides a good relevancy model, we may hope that the search process will be guided towards the best areas of the Web. Various studies have been carried out in this direction: for example, limiting the search depth in a site by specifying that pages are no longer relevant after a certain depth. This amounts to the following equation: s (depth) (u) = 1, if |root(u) u| < 0, else (2) where root(u) is the root of the site containing u. The interest of this approach lies in the fact that maximizing the search breadth may make it easier for the end-user to retrieve the information. Nevertheless, pages that are too deep may be accessed by the user, even if the robot fails to take them into account. A second possibility is the estimation of a page's popularity . One method of calculating a document's relevancy would relate to the number of backlinks. s (backlinks) (u) = 1, if indegree(u) > 0, else (3) where is a threshold. It is clear that s (backlinks) (u) may only be calculated if we have a complete site graph (site already downloaded beforehand). In practice, we make take an approximate value and update it incrementally during the crawling process. A derivative of this technique is used in Google's famous PageRank calculation. OUR APPROACH THE DOMINOS SYSTEM As mentioned above, we have divided the system into two parts: workers and supervisors. All of these processes may be run on various operating systems (Windows, MacOS X, Linux, FreeBSD) and may be replicated if need be. The workers are responsible for processing the URL flow coming from their supervisors and for executing crawling process tasks in the strict sense. They also handle the resolution of domain names by means of their integrated DNS resolver, and adjust download speed in accordance with node policy. A worker is a light process in the Erlang sense, acting as a fault tolerant and highly available HTTP client. The process-handling mode in Erlang makes it possible to create several thousands of workers in parallel. In our system, communication takes place mainly by sending asynchronous messages as described in the specifications for Erlang language. The type of message varies according to need: character string for short messages and binary format for long messages (large data structures or files). Disk access is reduced to a minimum as far as possible and structures are stored in the real-time Mnesia 3 database that forms 3 http://www.erlang.org/doc/r9c/lib/mnesia-4 .1.4/doc/html/ 301 a standard part of the Erlang development kit. Mnesia's features give it a high level of homogeneity during the base's access, replication and deployment. It is supported by two table management modules ETS and DETS. ETS allows tables of values to be managed by random access memory, while DETS provides a persistent form of management on the disk. Mnesia's distribution faculty provides an efficient access solution for distributed data. When a worker moves from one node to another (code migration), it no longer need be concerned with the location of the base or data. It simply has to read and write the information transparently. 1 loop(InternalState) -> % Supervisor main 2 % loop 3 receive {From,{migrate,Worker,Src,Dest}} -> 4 % Migrate the Worker process from 5 % Src node to Dest node 6 spawn(supervisor,migrate, 7 [Worker,Src,Dest]), 8 % Infinite loop 9 loop(InternalState); 10 11 {From,{replace,OldPid,NewPid,State}} -> 12 % Add the new worker to 13 % the supervisor state storage 14 NewInternalState = 15 replace(OldPid,NewPid,InternalState), 16 % Infinite loop 17 loop(NewInternalState); 18 ... 19 end. 20 21 migrate(Pid,Src,Dest) -> % Migration 22 % process 23 receive 24 Pid ! {self(), stop}, 25 receive 26 {Pid,{stopped,LastState}} -> 27 NewPid = spawn{Dest,worker,proc, 28 [LastState]}, 29 self() ! {self(), {replace,Pid, 30 NewPid,LastState}}; 31 {Pid,Error} -> ... 32 end. Listing 1: Process Migration Code 1describes the migration of a worker process from one node Src to another Dest. 4 The supervisor receives the migration order for process P id (line 4). The migration action is not blocking and is performed in a different Erlang process (line 7). The supervisor stops the worker with the identifier P id (line 25) and awaits the operation result (line 26). It then creates a remote worker in the node Dest with the latest state of the stopped worker (line 28) and updates its internal state (lines 30 and 12). 3.1 Dominos Process The Dominos system is different from all the other crawling systems cited above. Like these, the Dominos offering is on distributed architecture, but with the difference of being totally dynamic. The system's dynamic nature allows its architecture to be changed as required. If, for instance, one of the cluster's nodes requires particular maintenance, all of the processes on it will migrate from this node to another. When servicing is over, the processes revert automatically 4 The character % indicates the beginning of a comment in Erlang. to their original node. Crawl processes may change pool so as to reinforce one another if necessary. The addition or deletion of a node in the cluster is completely transparent in its execution. Indeed, each new node is created containing a completely blank system. The first action to be undertaken is to search for the generic server in order to obtain the parameters of the part of the system that it is to belong to. These parameters correspond to a limited view of the whole system. This enables Dominos to be deployed more easily, the number of messages exchanged between processes to be reduced and allows better management of exceptions. Once the generic server has been identified, binaries are sent to it and its identity is communicated to the other nodes concerned. Dominos Generic Server (GenServer): Erlang process responsible for managing the process identifiers on the whole cluster. To ensure easy deployment of Dominos, it was essential to mask the denominations of the process identifiers. Otherwise, a minor change in the names of machines or their IP would have required complete reorganization of the system. GenServer stores globally the identifiers of all processes existing at a given time. Dominos RPC Concurrent (cRPC): as its name suggests , this process is responsible for delegating the execution of certain remote functions to other processes . Unlike conventional RPCs where it is necessary to know the node and the object providing these functions (services), our RPCC completely masks the information. One need only call the function, with no concern for where it is located in the cluster or for the name of the process offering this function. Moreover, each RPCC process is concurrent, and therefore manages all its service requests in parallel. The results of remote functions are governed by two modes: blocking or non-blocking. The calling process may therefore await the reply of the remote function or continue its execution. In the latter case, the reply is sent to its mailbox. For example, no worker knows the process identifier of its own supervisor. In order to identify it, a worker sends a message to the process called supervisor. The RPCC deals with the message and searches the whole cluster for a supervisor process identifier, starting with the local node. The address is therefore resolved without additional network overhead, except where the supervisor does not exist locally. Dominos Distributed Database (DDB): Erlang process responsible for Mnesia real-time database management . It handles the updating of crawled information, crawling progress and the assignment of URLs to be downloaded to workers. It is also responsible for replicating the base onto the nodes concerned and for the persistency of data on disk. Dominos Nodes: a node is the physical representation of a machine connected (or disconnected as the case may be) to the cluster. This connection is considered in the most basic sense of the term, namely a simple plugging-in (or unplugging) of the network outlet. Each node clearly reflects the dynamic character of the Dominos system. 302 Dominos Group Manager: Erlang process responsible for controlling the smooth running of its child processes (supervisor and workers). Dominos Master-Supervisor Processes: each group manager has a single master process dealing with the management of crawling states of progress. It therefore controls all the slave processes (workers) contained within it. Dominos Slave-Worker Processes: workers are the lowest-level elements in the crawling process. This is the very heart of the Web client wrapping the libCURL. With Dominos architecture being completely dynamic and distributed, we may however note the hierarchical character of processes within a Dominos node. This is the only way to ensure very high fault tolerance. A group manager that fails is regenerated by the node on which it depends. A master process (supervisor) that fails is regenerated by its group manager. Finally, a worker is regenerated by its supervisor. As for the node itself, it is controlled by the Dominos kernel (generally on another remote machine). The following code describes the regeneration of a worker process in case of failure. 1 % Activate error handling 2 process_flag(trap_exit, true ), 3 ... 4 loop(InternalState) -> % Supervisor main loop 5 receive 6 {From,{job, Name ,finish}, State} -> 7 % Informe the GenServer that the download is ok 8 ?ServerGen ! {job, Name ,finish}, 9 10 % Save the new worker state 11 NewInternalState=save_state(From,State,InternalState), 12 13 % Infinite loop 14 loop(NewInternalState); 15 ... 16 {From,Error} -> % Worker crash 17 % Get the last operational state before the crash 18 WorkerState = last_state(From,InternalState), 19 20 % Free all allocated resources 21 free_resources(From,InternalState), 22 23 % Create a new worker with the last operational 24 % state of the crashed worker 25 Pid = spawn(worker,proc,[WorkerState]), 26 27 % Add the new worker to the supervisor state 28 % storage 29 NewInternalState =replace(From,Pid,InternalState), 30 31 % Infinite loop 32 loop(NewInternalState); 33 end. Listing 2: Regeneration of a Worker Process in Case of Failure This represents the part of the main loop of the supervisor process dealing with the management of the failure of a worker. As soon as a worker error is received (line 19), the supervisor retrieves the last operational state of the worker that has stopped (line 22), releases all of its allocated resources (line 26) and recreates a new worker process with the operational state of the stopped process (line 31). The supervisor continually turns in loop while awaiting new messages (line 40). The loop function call (lines 17 and 40) is tail recursive, thereby guaranteeing that the supervision process will grow in a constant memory space. 3.2 DNS Resolution Before contacting a Web server, the worker process needs to convert the Domain Name Server (DNS) into a valid IP address. Whereas other systems (Mercator, Internet Archive) are forced to set up DNS resolvers each time a new link is identified, this is not necessary with Dominos. Indeed, in the framework of French Web legal deposit, the sites to be archived have been identified beforehand, thus requiring only one DNS resolution per domain name. This considerably increases crawl speed. The sites concerned include all online newspapers , such as LeMonde (http://www.lemonde.fr/ ), LeFigaro (http://www.lefigaro.fr/ ) . . . , online television/radio such as TF1(http://www.tf1.fr/ ), M6 (http://www.m6.fr/ ) . . . DETAILS OF IMPLEMENTATION The workers are the medium responsible for physically crawling on-line contents. They provide a specialized wrapper around the libCURL 5 library that represents the heart of the HTTP client. Each worker is interfaced to libCURL by a C driver (shared library). As the system seeks maximum network accessibility (communication protocol support), libCURL appeared to be the most judicious choice when compared with other available libraries. 6 . The protocols supported include: FTP, FTPS, HTTP, HTTPS, LDAP, Certifications, Proxies, Tunneling etc. Erlang's portability was a further factor favoring the choice of libCURL. Indeed, libCURL is available for various architectures: Solaris, BSD, Linux, HPUX, IRIX, AIX, Windows, Mac OS X, OpenVMS etc. Furthermore, it is fast, thread-safe and IPv6 compatible. This choice also opens up a wide variety of functions. Redirections are accounted for and powerful filtering is possible according to the type of content downloaded, headers, and size (partial storage on RAM or disk depending on the document's size). 4.2 Document Fingerprint For each download, the worker extracts the hypertext links included in the HTML documents and initiates a fingerprint (signature operation). A fast fingerprint (HAVAL on 256 bits) is calculated for the document's content itself so as to differentiate those with similar contents (e.g. mirror sites). This technique is not new and has already been used in Mercator[13]. It allows redundancies to be eliminated in the archive. 4.3 URL Extraction and Normalization Unlike other systems that use libraries of regular expressions such as PCRE 7 for URL extraction, we have opted 5 Available at http://curl.haxx.se/libcurl/ 6 See http://curl.haxx.se/libcurl/competitors.html 7 Available at http://www.pcre.org/ 303 for the Flex tool that definitely generates a faster parser. Flex was compiled using a 256Kb buffer in which all table compression options were activated during parsing "-8 -f Cf -Ca -Cr -i". Our current parser analyzes around 3,000 pages/second for a single worker for an average 49Kb per page. According to [20], a URL extraction speed of 300 pages/second may generate a list of more than 2,000 URLs on average. A naive representation of structures in the memory may soon saturate the system. Various solutions have been proposed to alleviate this problem. The Internet Archive [4] crawler uses Bloom filters in random access memory. This makes it possible to have a compact representation of links retrieved, but also generates errors (false-positive), i.e. certain pages are never downloaded as they create collisions with other pages in the Bloom filter. Compression without loss may reduce the size of URLs to below 10Kb [2, 21], but this remains insufficient in the case of large-scale crawls. A more ingenious approach is to use persistent structures on disk coupled with a cache as in Mercator [13]. 4.4 URL Caching In order to speed up processing, we have developed a scalable cache structure for the research and storage of URLs already archived. Figure 1describes how such a cache works: Links Local Cache - Worker Rejected Links 0 1 2 255 JudyL-Array URL CRC URL #URL key value JudySL-Array Figure 1: Scalable Cache The cache is available at the level of each worker. It acts as a filter on URLs found and blocks those already encountered. The cache needs to be scalable to be able to deal with increasing loads. Rapid implementation using a non-reversible hash function such as HAVAL, TIGER, SHA1 , GOST, MD5, RIPEMD . . . would be fatal to the system's scalability. Although these functions ensure some degree of uniqueness in fingerprint constructionthey are too slow to be acceptable in these constructions. We cannot allow latency as far as lookup or URL insertion in the cache is concerned, if the cache is apt to exceed a certain size (over 10 7 key-value on average). This is why we have focused on the construction of a generic cache that allows key-value insertion and lookup in a scalable manner. The Judy-Array API 8 enabled us to achieve this objective. Without going into detail about Judy-Array (see their site for more information), our cache is a coherent coupling between a JudyL-Array and N JudySL-Array. The JudyL-Array represents a hash table of N = 2 8 or N = 2 16 buckets able to fit into the internal cache of the CPU. It is used to store "key-numeric value" pairs where the key represents a CRC of the 8 Judy Array at the address: http://judy.sourceforge.net/ URL and whose value is a pointer to a JudySL-Array. The second, JudySL-Array, is a "key-compressed character string value" type of hash, in which the key represents the URL identifier and whose value is the number of times that the URL has been viewed. This cache construction is completely scalable and makes it possible to have sub-linear response rates, or linear in the worst-case scenario (see Judy-Array at for an in-depth analysis of their performance). In the section on experimentation (section 5) we will see the results of this type of construction. 4.5 Limiting Disk Access Our aim here is to eliminate random disk access completely . One simple idea used in [20] is periodically to switch structures requiring much memory over onto disk. For example, random access memory can be used to keep only those URLs found most recently or most frequently, in order to speed up comparisons. This requires no additional development and is what we have decided to use. The persistency of data on disk depends on the size of data in DS memory, and their DA age. The data in the memory are distributed transparently via Mnesia, specially designed for this kind of situation. Data may be duplicated ( {ram copies, [Nodes]}, {disc copies, [Nodes]}) or fragmented ( {frag properties, .....}) on the nodes in question. According to [20], there are on average 8 non-duplicated hypertext links per page downloaded. This means that the number of pages retrieved and not yet archived is considerably increased. After archiving 20 million pages, over 100 million URLs would still be waiting. This has various repercussions, as newly-discovered URLs will be crawled only several days, or even weeks, later. Given this speed, the base's data refresh ability is directly affected. 4.6 High Availability In order to apprehend the very notion of High Availability, we first need to tackle the differences that exist between a system's reliability and its availability. Reliability is an attribute that makes it possible to measure service continuity when no failure occurs. Manufacturers generally provide a statistical estimation of this value for this equipment: we may use the term MTBF (Mean Time Between Failure). A strong MTBF provides a valuable indication of a component's ability to avoid overly frequent failure. In the case of a complex system (that can be broken down into hardware or software parts), we talk about MTTF (Mean Time To Failure). This denotes the average time elapsed until service stops as the result of failure in a component or software. The attribute of availability is more difficult to calculate as it includes a system's ability to react correctly in case of failure in order to restart service as quickly as possible. It is therefore necessary to quantify the time interval during which service is unavailable before being re-established: the acronym MTTR (Mean Time To Repair) is used to represent this value. The formula used to calculate the rate of a system's availability is as follows: availability = M T T F M T T F + M T T R (4) 304 A system that looks to have a high level of availability should have either a strong MTTF, or a weak MTTR. Another more practical approach consists in measuring the time period during which service is down in order to evaluate the level of availability. This is the method most frequently adopted, even if it fails to take account of the frequency of failure, focusing rather on its duration. Calculation is usually based on a calendar year. The higher the percentage of service availability, the nearer it comes to High Availability. It is fairly easy to qualify the level of High Availability of a service from the cumulated downtime, by using the normalized principle of "9's" (below 3 nine, we are no longer talking about High Availability, but merely availability). In order to provide an estimation of Dominos' High Availability, we carried out performance tests by fault injection. It is clear that a more accurate way of measuring this criterion would be to let the system run for a whole year as explained above. However, time constraints led us to adopt this solution. Our injector consists in placing pieces of false code in each part of the system and then measuring the time required for the system to make the service available. Once again, Erlang has proved to be an excellent choice for the setting up of these regression tests. The table below shows the average time required by Dominos to respond to these cases of service unavailability. Table 1clearly shows Dominos' High Availability. We Service Error MTTR (microsec) GenServer 10 3 bad match 320 cRPC 10 3 bad match 70 DDB 10 7 tuples 9 10 6 Node 10 3 bad match 250 Supervisor 10 3 bad match 60 Worker 10 3 bad match 115 Table 1: MTTR Dominos see that for 10 3 matches of error, the system resumes service virtually instantaneously. The DB was tested on 10 7 tuples in random access memory and resumed service after approximately 9 seconds. This corresponds to an excellent MTTR, given that the injections were made on a PIII-966Mhz with 512Mb of RAM. From these results, we may label our system as being High Availability, as opposed to other architectures that consider High Availability only in the sense of failure not affecting other components of the system, but in which service restart of a component unfortunately requires manual intervention every time. EXPERIMENTATION This section describes Dominos' experimental results tested on 5 DELL machines: nico: Intel Pentium 4 - 1.6 Ghz, 256 Mb RAM. Crawl node (supervisor, workers). Activates a local cRPC. zico: Intel Pentium 4 - 1.6 Ghz, 256 Mb RAM. Crawl node (supervisor, workers). Activates a local cRPC. chopin: Intel Pentium 3 - 966 Mhz, 512 Mb RAM. Main node loaded on ServerGen and DB. Also handles crawling (supervisor, workers). Activates a local cRPC. gao: Intel Pentium 3 - 500 Mhz, 256 Mb RAM. Node for DB fragmentation. Activates a local cRPC. margo: Intel Pentium 2 - 333 Mhz, 256 Mb RAM. Node for DB fragmentation. Activates a local cRPC. Machines chopin, gao and margo are not dedicated solely to crawling and are used as everyday workstations. Disk size is not taken into account as no data were actually stored during these tests. Everything was therefore carried out using random access memory with a network of 100 Mb/second. Dominos performed 25,116,487 HTTP requests after 9 hours of crawling with an average of 816 documents/second for 49Kb per document. Three nodes (nico, zico and chopin) were used in crawling, each having 400 workers. We restricted ourselves to a total of 1,200 workers, due to problems generated by Dominos at intranet level. The firewall set up to filter access is considerably detrimental to performance because of its inability to keep up with the load imposed by Dominos. Third-party tests have shown that peaks of only 4,000 HTTP requests/second cause the immediate collapse of the firewall. The firewall is not the only limiting factor, as the same tests have shown the incapacity of Web servers such as Apache2, Caudium or Jigsaw to withstand such loads (see http://www.sics.se/ joe/apachevsyaws.html). Figure 2 (left part) shows the average URL extraction per document crawled using a single worker. The abscissa (x) axis represents the number of documents treated, and the ordered (y) axis gives the time in microseconds corresponding to extraction. In the right-hand figure, the abscissa axis represents the same quantity, though this time in terms of data volume (Mb). We can see a high level of parsing reaching an average of 3,000 pages/second at a speed of 70Mb/second. In Figure 3 we see that URL normalization 0 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 0 2000 4000 6000 8000 10000 Time (microsec) Documents Average number of parsed documents PD 0 500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 0 20 40 60 80 100 120 140 160 Time (microsec) Document Size (Mb) Average size of parsed documents PDS Figure 2: Link Extraction is as efficient as extraction in terms of speed. The abscissa axis at the top (and respectively at the bottom) represents the number of documents processed per normalization phase (respectively the quantity of documents in terms of volume). Each worker normalizes on average 1,000 documents/second , which is equivalent to 37,000 URLs/second at a speed of 40Mb/second. Finally, the URL cache structure ensures a high degree of scalability (Figure 3). The abscissa axis in this figure represents the number of key-values inserted or retrieved. The cache is very close to a step function due to key compression in the Judy-Array. Following an increase in insertion/retrieval time in the cache, it appears to plateau by 100,000 key-value bands. We should however point out that URL extraction and normalization also makes use of this type of cache so as to avoid processing a URL already encountered. 305 0 10000 20000 30000 40000 50000 60000 0 2000 4000 6000 8000 10000 Time (microsec) Normalized documents Average number of normalized documents AD 0 10000 20000 30000 40000 50000 60000 0 2000 4000 6000 8000 10000 12000 14000 16000 Time (microsec) Urls Average number of normalized Url AU 0 10000 20000 30000 40000 50000 60000 0 20 40 60 80 100 120 140 160 Time (microsec) Document Size (Mb) Average size of normalized documents ADS 0 50000 100000 150000 200000 250000 300000 350000 0 20000 40000 60000 80000 100000 Time (microsec) Key-Value Scalable Cache : Insertion vs Retrieval Cache Insertion Cache Retrieval Figure 3: URL Normalization and Cache Performance CONCLUSION In the present paper, we have introduced a high availability system of crawling called Dominos. This system has been created in the framework of experimentation for French Web legal deposit carried out at the Institut National de l'Audiovisuel (INA). Dominos is a dynamic system, whereby the processes making up its kernel are mobile. 90% of this system was developed using Erlang programming language, which accounts for its highly flexible deployment, maintainability and enhanced fault tolerance. Despite having different objectives, we have been able to compare it with other documented Web crawling systems (Mercator, InternetArchive . . . ) and have shown it to be superior in terms of crawl speed, document parsing and process management without system restart. Dominos is more complex than its description here. We have not touched upon archival storage and indexation. 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Science 280, pages 98100, 1998. [17] M. Najork and J. Wiener. Breadth-first search crawling yields high-quality pages. In 10th Int. World Wide Web Conference, 2001. [18] J. Rennie and A. McCallum. Using reinforcement learning to spider the web efficiently. In Proc. of the Int. Conf. on Machine Learning, 1999. [19] S. Russel and P. Norvig. Artificial Intelligence: A modern Approach. Prentice Hall, 1995. [20] V. Shkapenyuk and T. Suel. Design and implementation of a high-performance distributed web crawler. Polytechnic University: Brooklyn, Mars 2001. [21] T. Suel and J. Yuan. Compressing the graph structure of the web. In Proc. of the IEEE Data Compression Conference, 2001. [22] J. Talim, Z. Liu, P. Nain, and E. Coffman. Controlling robots of web search engines. In SIGMETRICS Conference, 2001. 306

Breadth first crawling;Hierarchical Cooperation;limiting disk access;fault tolerance;Dominos nodes;dominos process;Dominos distributed database;breadth-first crawling;repetitive crawling;URL caching;Dominos Generic server;Document fingerprint;Deep web crawling;Dominos RPC concurrent;Random walks and sampling;Web Crawler;maintaiability and configurability;deep web crawling;High Availability System;real-time distributed system;crawling system;high performance crawling system;high availability;Erlang development kit;targeted crawling

101

Hiperlan/2 Public Access Interworking with 3G Cellular Systems

This paper presents a technical overview of the Hiperlan/2 3G interworking concept. It does not attempt to provide any business justification or plan for Public Access operation. After a brief resume of public access operation below, section 2 then introduces an overview of the technologies concerned. Section 3 describes the system approach and presents the current reference architecture used within the BRAN standardisation activity. Section 4 then goes on to cover in more detail the primary functions of the system such as authentication, mobility, quality of service (QoS) and subscription. It is worth noting that since the Japanese WLAN standard HiSWANa is very similar to Hiperlan/2, much of the technical information within this paper is directly applicable to this system, albeit with some minor changes to the authentication scheme. Additionally the high level 3G and external network interworking reference architecture is also applicable to IEEE 802.11. Finally, section 5 briefly introduces the standardisation relationships between ETSI BRAN, WIG, 3GPP, IETF, IEEE 802.11 and MMAC HSWA.

1.1. Public access operation Recently, mobile business professionals have been looking for a more efficient way to access corporate information systems and databases remotely through the Internet backbone. However, the high bandwidth demand of the typical office applications , such as large email attachment downloading, often calls for very fast transmission capacity. Indeed certain hot spots, like hotels, airports and railway stations are a natural place to use such services. However, in these places the time available for information download typically is fairly limited. In light of this, there clearly is a need for a public wireless access solution that could cover the demand for data intensive applications and enable smooth on-line access to corporate data services in hot spots and would allow a user to roam from a private, micro cell network (e.g., a Hiperlan/2 Network) to a wide area cellular network or more specifically a 3G network. Together with high data rate cellular access, Hiperlan/2 has the potential to fulfil end user demands in hot spot environments . Hiperlan/2 offers a possibility for cellular operators to offer additional capacity and higher bandwidths for end users without sacrificing the capacity of the cellular users, as Hiperlans operate on unlicensed or licensed exempt frequency bands. Also, Hiperlan/2 has the QoS mechanisms that are capable to meet the mechanisms that are available in the 3G systems. Furthermore, interworking solutions enable operators to utilise the existing cellular infrastructure investments and well established roaming agreements for Hiperlan/2 network subscriber management and billing. Technology overview This section briefly introduces the technologies that are addressed within this paper. 2.1. Hiperlan/2 summary Hiperlan/2 is intended to provide local wireless access to IP, Ethernet, IEEE 1394, ATM and 3G infrastructure by both stationary and moving terminals that interact with access points. The intention is that access points are connected to an IP, Ethernet , IEEE 1394, ATM or 3G backbone network. A number of these access points are required to service all but the small-44 MCCANN AND FLYGARE est networks of this kind, and therefore the wireless network as a whole supports handovers of connections between access points. 2.2. Similar WLAN interworking schemes It should be noted that the interworking model presented in this paper is also applicable to the other WLAN systems, i.e. IEEE 802.11a/b and MMAC HiSWANa (High Speed Wireless Access Network), albeit with some minor modifications to the authentications schemes. It has been the intention of BRAN to produce a model which not only fits the requirements of Hiperlan/23G interworking, but also to try and meet those of the sister WLAN systems operating in the same market. A working agreement has been underway between ETSI BRAN and MMAC HSWA for over 1 year, and with the recent creation of WIG (see section 5), IEEE 802.11 is also working on a similar model. 2.3. 3G summary Within the framework of International Mobile Telecommunications 2000 (IMT-2000), defined by the International Telecommunications Union (ITU), the 3rd Generation Partnership Project (3GPP) are developing the Universal Mobile Telecommunications System (UMTS) which is one of the major third generation mobile systems. Additionally the 3rd Generation Partnership Project 2 (3GPP2) is also developing another 3G system, Code Division Multiple Access 2000 (CDMA-2000). Most of the work within BRAN has concentrated on UMTS, although most of the architectural aspects are equally applicable to Hiperlan/2 interworking with CDMA-2000 and indeed pre-3G systems such as General Packet Radio Services (GPRS). The current working UMTS standard, Release 4, of UMTS was finalised in December 2000 with ongoing development work contributing to Release 5, due to be completed by the end of 2002. A future release 6 is currently planned for the autumn of 2003, with worldwide deployment expected by 2005. System approach This section describes the current interworking models being worked upon within BRAN at the current time. The BRAN Network Reference Architecture, shown in figure 1, identifies the functions and interfaces that are required within a Hiperlan/2 network in order to support inter-operation with 3G systems . The focus of current work is the interface between the Access Point (AP) and the Service provider network (SPN) which is encapsulated by the Lx interface. The aim of the Hiperlan/23G interworking work item is to standardise these interfaces, initially focusing on AAA (Authentication, Authorisation and Accounting) functionality. A secondary aim is to create a model suitable for all the 5 GHz WLAN systems (e.g., Hiperlan/2, HiSWANa, IEEE Figure 1. Reference architecture. 802.11a) and all 3G systems (e.g., CDMA-2000, UMTS), thus creating a world wide standard for interworking as mentioned in section 5. Other interfaces between the AP and external networks and interfaces within the AP are outside the scope of this current work. Figure 1 shows the reference architecture of the interworking model. It presents logical entities within which the following functions are supported: Authentication: supports both SIM-based and SIM-less authentication. The mobile terminal (MT) communicates via the Attendant with an authentication server in the visited network, for example a local AAA server, across the Ls interface. Authorisation and User Policy: the SPN retrieves authorisation and user subscription information from the home network when the user attaches to it. Authorisation information is stored within a policy decision function in the SPN. Interfaces used for this are Lp and Ls. Accounting: the resources used by a MT and the QoS provided to a user are both monitored by the Resource Monitor . Accounting records are sent to accounting functions in the visited network via the La interface. Network Management: the Management Agent provides basic network and performance monitoring, and allows the configuration of the AP via the Lm interface. Admission Control and QoS: a policy decision function in the SPN decides whether a new session with a requested QoS can be admitted based on network load and user subscription information. The decision is passed to the Policy Enforcement function via the Lp interface. Inter-AP Context Transfer: the Handover Support function allows the transfer of context information concerning a user/mobile node, e.g., QoS state, across the Lh interface from the old to the new AP between which the mobile is handing over. HIPERLAN/2 PUBLIC ACCESS INTERWORKING WITH 3G CELLULAR SYSTEMS 45 Mobility: mobility is a user plane function that performs re-routing of data across the network. The re-routing may simply be satisfied by layer 2 switching or may require support for a mobility protocol such as Mobile IP depending on the technology used within the SPN. Mobility is an attribute of the Lr interface. Location Services: the Location Server function provides positioning information to support location services. Information is passed to SPN location functions via the Ll interface. Primary functions This section describes the primary functions of this model (refer to figure 1) in further detail, specifically: authentication and accounting, mobility and QoS. 4.1. Authentication and authorisation A key element to the integration of disparate systems is the ability of the SPN to extract both authentication and subscription information from the mobile users' home networks when an initial association is requested. Many users want to make use of their existing data devices (e.g., Laptop, Palmtop) without additional hardware/software requirements. Conversely for both users and mobile operators it is beneficial to be able to base the user authentication and accounting on existing cellular accounts, as well as to be able to have Hiperlan/2-only operators and users; in any case, for reasons of commonality in MT and network (indeed SPN) development it is important to be able to have a single set of AAA protocols which supports all the cases. 4.1.1. Loose coupling The rest of this paper concentrates on loose coupling solutions . "Loose coupling", is generally defined as the utilisation of Hiperlan/2 as a packet based access network complementary to current 3G networks, utilising the 3G subscriber databases but without any user plane Iu type interface, as shown in figure 1. Within the UMTS context, this scheme avoids any impact on the SGSN and GGSN nodes. Security, mobility and QoS issues are addressed using Internet Engineering Task Force (IETF) schemes. Other schemes which essentially replace the User Terminal Radio Access Network (UTRAN) of UMTS with a HIRAN (Hiperlan Radio Access Network) are referred to as "Tight Coupling", but are not currently being considered within the work of BRAN. 4.1.2. Authentication flavours This section describes the principle functions of the loose coupling interworking system and explains the different authentication flavours that are under investigation. The focus of current work is the interface between the AP and the SPN. Other interfaces between the AP and external networks and interfaces within the AP are initially considered to be implementation or profile specific. The primary difference between these flavours is in the authentication server itself, and these are referred to as the "IETF flavour" and the "UMTS-HSS flavour", where the Home Subscriber Server (HSS) is a specific UMTS term for a combined AAA home server (AAAH)/Home Location Register (HLR) unit. The motivation for network operators to build up Hiperlan/2 networks based on each flavour may be different for each operator. However, both flavours offer a maximum of flexibility through the use of separate Interworking Units (IWU) and allow loose coupling to existing and future cellular mobile networks. These alternatives are presented in figure 2. IETF flavour. The IETF flavour outlined in figure 2 is driven by the requirement to add only minimal software functionality to the terminals (e.g., by downloading java applets), so that the use of a Hiperlan/2 mobile access network does not require a radical change in the functionality (hardware or software ) compared to that required by broadband wireless data access in the corporate or home scenarios. Within a multiprovider network, the WLAN operator (who also could be a normal ISP) does not necessary need to be the 3G operator as well, but there could still be an interworking between the networks. Within this approach Hiperlan/2 users may be either existing 3G subscribers or just Hiperlan/2 network subscribers. These users want to make use of their existing data devices (e.g., Laptop, Palmtop) without additional hardware/software requirements. For both users and mobile operators it is beneficial to be able to base the user authentication and accounting on existing cellular accounts, as well as to be able to have Hiperlan/2-only operators and users; in any case, for reasons of commonality in MT and AP development it is important to be able to have a single set of AAA protocols which supports all the cases. UMTS-HSS flavour. Alternatively the UMTS flavour (also described within figure 1) allows a mobile subscriber using a Hiperlan/2 mobile access network for broadband wireless data access to appear as a normal cellular user employing standard procedures and interfaces for authentication purposes . It is important to notice that for this scenario functionality normally provided through a user services identity module (USIM) is required in the user equipment. The USIM provides new and enhanced security features in addition to those provided by 2nd Generation (2G) SIM (e.g., mutual authentication ) as defined by 3GPP (3G Partnership Program). The UMTS-HSS definitely requires that a user is a native cellular subscriber while in addition and distinctly from the IETF flavoured approach standard cellular procedures and parameters for authentication are used (e.g., USIM quintets). In this way a mobile subscriber using a Hiperlan/2 mobile access network for broadband wireless data access will appear as a normal cellular user employing standard procedures and interfaces for authentication purposes. It is important to notice that for this scenario USIM functionality is required in the user equipment. 46 MCCANN AND FLYGARE Figure 2. Loose coupling authentication flavours. For the IETF flavoured approach there is no need to integrate the Hiperlan/2 security architecture with the UMTS security architecture [2]. It might not even be necessary to implement all of the Hiperlan/2 security features if security is applied at a higher level, such as using IPsec at the IP level. An additional situation that must be considered is the use of pre-paid SIM cards. This scenario will introduce additional requirements for hot billing and associated functions. 4.1.3. EAPOH For either flavour authentication is carried out using a mechanism based on EAP (Extensible Authentication Protocol) [3]. This mechanism is called EAPOH (EAP over Hiperlan/2) and is analogous to the EAPOL (EAP over LANs) mechanism as defined in IEEE 802.1X. On the network side, Diameter [4] is used to relay EAP packets between the AP and AAAH. Between the AP and MT, EAP packets and additional Hiperlan/2 specific control packets (termed pseudo-EAP packets) are transferred over the radio interface. This scheme directly supports IETF flavour authentication, and by use of the pro-posed EAP AKA (Authentication and Key Agreement) mechanism would also directly support the UMTS flavour authentication . Once an association has been established, authorisation information (based on authentication and subscription) stored within a Policy Decision Function within the SPN itself can be transmitted to the AP. This unit is then able to regulate services such as time-based billing and allocation of network and radio resources to the required user service. Mobile users with different levels of subscription (e.g., "bronze, silver, gold") can be supported via this mechanism, with different services being configured via the policy interface. A change in authentication credentials can also be managed at this point. 4.1.4. Key exchange Key agreement for confidentiality and integrity protection is an integral part of the UMTS authentication procedure, and hence the UTRAN confidentiality and integrity mechanisms should be reused within the Hiperlan/2 when interworking with a 3G SPN (i.e. core network). This will also increase the applied level of security. The Diffie-Hellman encryption key agreement procedure, as used by the Hiperlan/2 air interface, could be used to improve user identity confidentiality. By initiating encryption before UMTS AKA is performed, the user identity will not have to be transmitted in clear over the radio interface, as is the case in UMTS when the user enters a network for the first time. Thus, this constitutes an improvement compared to UMTS security. It is also important to have a secure connection between APs within the same network if session keys or other sensitive information are to be transferred between them. A secure connection can either be that they for some reason trust each other and that no one else can intercept the communication between them or that authentication is performed and integrity and confidentiality protection are present. 4.1.5. Subscriber data There are three basic ways in which the subscriber management for Hiperlan/2 and 3G users can be co-ordinated: Have the interworking between the Hiperlan/2 subscriber database and HLR/HSS. This is for the case where the in-HIPERLAN/2 PUBLIC ACCESS INTERWORKING WITH 3G CELLULAR SYSTEMS 47 terworking is managed through a partnership or roaming agreement. The administrative domains' AAA servers share security association or use an AAA broker. The Hiperlan/2 authentication could be done on the basis of a (U)SIM token. The 3G authentication and accounting capabilities could be extended to support access authentication based on IETF protocols. This means either integrating HLR and AAA functions within one unit (e.g., a HSS unit), or by merging native HLR functions of the 3G network with AAA functions required to support IP access. Based on these different ways for subscriber management, the user authentication identifier can be on three different formats : Network Address Identifier (NAI), International Mobile Subscriber Identity (IMSI) (requires a (U)SIM card), and IMSI encapsulated within a NAI (requires a (U)SIM card). 4.1.6. Pre-paid SIM cards As far as the HLR within the SPN is concerned, it cannot tell the difference between a customer who is pre-paid or not. Hence, this prevents a non-subscriber to this specific 3G network from using the system, if the operator wishes to impose this restriction. As an example, pre-paid calls within a 2G network are handled via an Intelligent Network (IN) probably co-located with the HLR. When a call is initiated, the switch can be pro-grammed with a time limit, or if credit runs out the IN can signal termination of the call. This then requires that the SPN knows the remaining time available for any given customer. Currently the only signals that originate from the IN are to terminate the call from the network side. This may be undesirable in a Hiperlan/23G network, so that a more graceful solution is required. A suitable solution is to add pre-paid SIM operation to our system together with hot billing (i.e. bill upon demand) or triggered session termination . This could be achieved either by the AAAL polling the SPN utilising RADIUS [5] to determine whether the customer is still in credit, or by using a more feature rich protocol such as Diameter [4] which allows network signalling directly to the MT. The benefit of the AAA approach is to allow the operator to present the mobile user with a web page (for example), as the pre-paid time period is about to expire, allowing them to purchase more airtime. All these solutions would require an increased integration effort with the SPN subscriber management system. Further additional services such as Customized Applications for Mobile Network Enhanced Logic (CAMEL) may also allow roaming with pre-paid SIM cards. 4.2. Accounting In the reference architecture of figure 2, the accounting function monitors the resource usage of a user in order to allow cost allocation, auditing and billing. The charging/accounting is carried out according to a series of accounting and resource monitoring metrics, which are derived from the policy function and network management information. The types of information needed in order to monitor each user's resource consumption could include parameters such as, for example, volume of traffic, bandwidth consumption, etc. Each of these metrics could have AP specific aspects concerning the resources consumed over the air interface and those consumed across the SPN, respectively. As well as providing data for billing and auditing purposes, this information is exchanged with the Policy Enforcement/Decision functions in order to provide better information on which to base policy decisions. The accounting function processes the usage related information including summarisation of results and the generation of session records. This information may then be forwarded to other accounting functions within and outside the network, for example a billing function. This information may also be passed to the Policy Decision function in order to improve the quality of policy decisions; vice versa the Policy Decision function can give information about the QoS, which may affect the session record. There are also a number of extensions and enhancements that can be made to the basic interworking functionality such as those for the provision of support for QoS and mobility. In a multiprovider network, different sorts of inter-relationships between the providers can be established. The inter-relationship will depend upon commercial conditions, which may change over time. Network Operators have exclusive agreements with their customers, including charging and billing, and also for services provided by other Network Op-erators/Service Providers. Consequently, it must be possible to form different charging and accounting models and this requires correspondent capabilities from the networks. Charging of user service access is a different issue from the issue of accounting between Network Operators and Service Providers. Although the issues are related, charging and accounting should be considered separately. For the accounting issue it is important for the individual Network Operator or Service Provider to monitor and register access use provided to his customers. Network operators and service providers that regularly provide services to the same customers could either charge and bill them individually or arrange a common activity. For joint provider charging/billing, the providers need revenue accounting in accordance with the service from each provider. For joint provider charging of users, it becomes necessary to transfer access/session related data from the providers to the charging entity. Mechanisms for revenue accounting are needed, such as technical configuration for revenue accounting . This leads to transfer of related data from the Network 48 MCCANN AND FLYGARE Operator and/or Service Providers to the revenue accounting entity. The following parameters may be used for charging and revenue accounting: basic access/session (pay by subscription), toll free (like a 0800 call), premium rate access/session, access/session duration, credit card access/session, pre-paid, calendar and time related charging, priority, Quality of Service, duration dependent charging, flat rate, volume of transferred packet traffic, rate of transferred packet traffic (Volume/sec), multiple rate charge. 4.3. Mobility Mobility can be handled by a number of different approaches. Indeed many mobility schemes have been developed in the IETF that could well be considered along with the work of the MIND (Mobile IP based Network Developments) project that has considered mobility in evolved IP networks with WLAN technologies. Mobility support is desirable as this functionality would be able to provide support for roaming with an active connection between the interworked networks, for example , to support roaming from UMTS to WLAN in a hotspot for the downloading of large data. In the loose coupling approach, the mobility within the Hiperlan/2 network is provided by native Hiperlan/2 (i.e. RLC layer) facilities, possibly extended by the Convergence Layer (CL) in use (e.g., the current Ethernet CL [6], or a future IP CL). This functionality should be taken unchanged in the loose coupling approach, i.e. handover between access points of the same Hiperlan/2 network does not need to be considered especially here as network handover capabilities of Hiperlan/2 RLC are supported by both MTs and APs. Given that Hiperlan/2 network handover is supported, further details for completing the mobility between access points are provided by CL dependent functionality. Completion of this functionality to cover interactions between the APs and other parts of the network (excluding the terminal and therefore independent of the air interface) are currently under development outside BRAN. In the special case where the infrastructure of a single Hiperlan/2 network spans more than one IP sub-network, some of the above approaches assume an additional level of mobility support that may involve the terminal. 4.3.1. Roaming between Hiperlan/2 and 3G For the case of mobility between Hiperlan/2 and 3G access networks, recall that we have the following basic scenario: A MT attaches to a Hiperlan/2 network, authenticates and acquires an IP address. At that stage, it can access IP services using that address while it remains within that Hiperlan/2 network . If the MT moves to a network of a different technology (i.e. UMTS), it can re-authenticate and acquire an IP address in the packet domain of that network, and continue to use IP services there. We have referred to this basic case as AAA roaming. Note that while it provides mobility for the user between networks, any active sessions (e.g., multimedia calls or TCP connections ) will be dropped on the handover between the networks because of the IP address change (e.g., use Dynamic Host Configuration Protocol DHCP). It is possible to provide enhanced mobility support, including handover between Hiperlan/2 access networks and 3G access networks in this scenario by using servers located outside the access network. Two such examples are: The MT can register the locally acquired IP address with a Mobile IP (MIP) home agent as a co-located care-of address , in which case handover between networks is handled by mobile IP. This applies to MIPv4 and MIPv6 (and is the only mode of operation allowed for MIPv6). The MT can register the locally acquired IP address with an application layer server such as a Session Initiation Protocol (SIP) proxy. Handover between two networks can then be handled using SIP (re-invite message). Note that in both these cases, the fact that upper layer mobility is in use is visible only to the terminal and SPN server, and in particular is invisible to the access network. Therefore, it is automatically possible, and can be implemented according to existing standards, without impact on the Hiperlan/2 network itself. We therefore consider this as the basic case for the loose coupling approach. Another alternative is the use of a Foreign Agent care-of address (MIPv4 only). This requires the integration of Foreign Agent functionality with the Hiperlan/2 network, but has the advantage of decreasing the number of IPv4 addresses that have to be allocated. On the other hand, for MTs that do not wish to invoke global mobility support in this case, a locally assigned IP address is still required, and the access network therefore has to be able to operate in two modes. Two options for further study are: The option to integrate access authentication (the purpose of this loose coupling standard) with Mobile IP home agent registration (If Diameter is used, it is already present). This would allow faster attach to the network in the case of a MT using MIP, since it only requires one set of authentication exchanges; however, it also requires integration on the control plane between the AAAH and the Mobile IP home agent itself. It is our current assumption that this integration should be carried out in a way that is independent of the particular access network being used, and is therefore out of scope of this activity. HIPERLAN/2 PUBLIC ACCESS INTERWORKING WITH 3G CELLULAR SYSTEMS 49 The implications of using services (e.g., SIP call control ) from the UMTS IMS (Internet Multimedia Subsys-tem ), which would provide some global mobility capability . This requires analysis of how the IMS would interface to the Hiperlan/2 access network (if at all). 4.3.2. Handover For handovers within the Hiperlan/2 network, the terminal must have enough information to be able to make a handover decision for itself, or be able to react to a network decision to handover. Indeed these decision driven events are referred to as triggers, resulting in Network centric triggers or Terminal centric triggers. Simple triggers include the following: Network Centric: Poor network resources or low bandwidth , resulting in poor or changing QoS. Change of policy based on charging (i.e. end of pre-paid time). Terminal Centric: Poor signal strength. Change of QoS. 4.4. QoS QoS support is available within the Hiperlan/2 specification but requires additional functionality in the interworking specifications for the provision of QoS through the CN rather than simply over the air. QoS is a key concept, within UMTS, and together with the additional QoS functionality in Hiperlan/2, a consistent QoS approach can therefore be provided. A number of approaches to QoS currently exist which still need to be considered at this stage. QoS within the Hiperlan/2 network must be supported between the MT and external networks, such as the Internet. In the loose coupling scenario, the data path is not constrained to travelling across the 3G SPN, e.g., via the SGSN/GGSNs. Therefore no interworking is required between QoS mechanisms used within the 3G and Hiperlan/2 network. There is a possible interaction regarding the interpretation and mapping of UMTS QoS parameters onto the QoS mechanisms used in the Hiperlan/2 network. The actual provisioning of QoS across the Hiperlan/2 network is dependent on the type of the infrastructure technology used, and therefore the capabilities of the CL. 4.4.1. HiperLAN2/Ethernet QoS mapping Within the Hiperlan/2 specification, radio bearers are referred to as DLC connections. A DLC connection is characterised by offering a specific support for QoS, for instance in terms of bandwidth, delay, jitter and bit error rate. The characteristics of supported QoS classes are implementation specific. A user might request for multiple DLC connections, each transferring a specific traffic type, which indicates that the traffic division is traffic type based and not application based. The DLC connection set-up does not necessarily result in immediate assignment of resources though. If the MT has not negotiated a fixed capacity agreement with the AP, it must request capacity by sending a resource request (RR) to the AP whenever it has data to transmit. The allocation of resources may thereby be very dynamic. The scheduling of the resources is vendor specific and is therefore not included in the Hiperlan/2 standard, which also means that QoS parameters from higher layers are not either. Hiperlan/2 specific QoS support for the DLC connection comprises centralised resource scheduling through the TDMA-based MAC structure, appropriate error control (acknowledged , unacknowledged or repetition) with associated protocol settings (ARQ window size, number of retransmis-sions and discarding), and the physical layer QoS support. Another QoS feature included in the Hiperlan/2 specification is a polling mechanism that enables the AP to regularly poll the MT for its traffic status, thus providing rapid access for real-time services. The CL acts as an integrator of Hiperlan/2 into different existing service provider networks, i.e. it connects the SPNs to the Hiperlan/2 data link control (DLC) layer. IEEE 802.1D specifies an architecture and protocol for MAC bridges interconnecting IEEE 802 LANs by relaying and filtering frames between the separate MACs of the Bridged LAN. The priority mechanism within IEEE 802.1D is handled by IEEE 802.1p, which is incorporated into IEEE 802.1D. All traffic types and their mappings presented in the tables of this section only corresponds to default values specified in the IEEE 802.1p standard, since these parameters are vendor specific. IEEE 802.1p defines eight different priority levels and describes the traffic expected to be carried within each priority level. Each IEEE 802 LAN frame is marked with a user priority (07) corresponding to the traffic type [8]. In order to support appropriate QoS in Hiperlan/2 the queues are mapped to the different QoS specific DLC connections (maximum of eight). The use of only one DLC connection between the AP and the MT results in best effort traffic only, while two to eight DLC connections indicates that the MT wants to apply IEEE 802.1p. A DLC connection ID is only MT unique, not cell unique. The AP may take the QoS parameters into account in the allocation of radio resources (which is out of the Hiperlan/2 scope). This means that each DLC connection, possibly operating in both directions, can be assigned a specific QoS, for instance in terms of bandwidth, delay, jitter and bit error rate, as well as being assigned a priority level relative to other DLC connections. In other words, parameters provided by the application, including UMTS QoS parameters if desired , are used to determine the most appropriate QoS level to be provided by the network, and the traffic flow is treated accordingly. The support for IEEE 802.1p is optional for both the MT and AP. 4.4.2. End-to-end based QoS Adding QoS, especially end-to-end QoS, to IP based connections raises significant alterations and concerns since it represents a digression from the "best-effort" model, which constitutes the foundation of the great success of Internet. However, the need for IP QoS is increasing and essential work is cur-50 MCCANN AND FLYGARE rently in progress. End-to-end IP QoS requires substantial consideration and further development. Since the Hiperlan/2 network supports the IEEE 802.1p priority mechanism and since Differentiated Services (DiffServ ) is priority based, the natural solution to the end-to-end QoS problem would be the end-to-end implementation of DiffServ. The QoS model would then appear as follows. QoS from the MT to the AP is supported by the Hiperlan/2 specific QoS mechanisms, where the required QoS for each connection is identified by a unique Data Link Control (DLC) connection ID. In the AP the DLC connection IDs may be mapped onto the IEEE 802.1p priority queues. Using the IEEE 802.1p priority mechanisms in the Ethernet, the transition to a DiffServ network is easily realised by mapping the IEEE 802.1p user priorities into DiffServ based priorities. Neither the DiffServ nor the IEEE 802.1p specification elaborates how a particular packet stream will be treated based on the Differentiated Services (DS) field and the layer 2 priority level. The mappings between the IEEE 802.1p priority classes and the DiffServ service classes are also unspec-ified . There is however an Integrated Services over Specific Link Layers (ISSLL) draft mapping for Guaranteed and Controlled Load services to IEEE 802.1p user priority, and a mapping for Guaranteed and Controlled Load services, to DiffServ which together would imply a DiffServ to IEEE 802.1p user priority mapping. DiffServ provides inferior support of QoS than IntServ, but the mobility of a Hiperlan/2 MT indicates a need to keep the QoS signalling low. IntServ as opposed to DiffServ involves significant QoS signalling. The DiffServ model provides less stringent support of QoS than the IntServ/RSVP model but it has the advantage over IntServ/RSVP of requiring less protocol signalling, which might be a crucial factor since the mobility of a Hiperlan/2 MT indicates a need to keep the QoS signalling low. Furthermore , the implementation of an end-to-end IntServ/RSVP based QoS architecture is much more complex than the implementation of a DiffServ based one. Discussions around end-to-end QoS support raise some critical questions that need to be considered and answered before a proper solution can be developed; which performance can we expect from the different end-to-end QoS models, what level of QoS support do we actually need, how much bandwidth and other resources are we willing to sacrifice on QoS, and how much effort do we want to spend on the process of developing well-supported QoS? Relationships with other standardisation bodies BRAN is continuing to have a close working relationship with the following bodies: WLAN Interworking Group (WIG) This group met for the first time in September 2002. Its broad aim is to provide a single point of contact for the three main WLAN standardisation bodies (ETSI BRAN, IEEE 802.11 and MMAC HSWA) and to produce a generic approach to both Cellular and external network interworking of WLAN technology. It has been also decided to work upon, complete and then share a common standard for WLAN Public Access and Cellular networks. 3rd Generation Partnership Project (3GPP) The System Architecture working group 1 (SA1) is currently developing a technical report detailed the requirements for a UMTSWLAN interworking system. They have defined 6 scenarios detailing aspects of differently coupled models, ranging from no coupling, through loose coupling to tight coupling. Group 2 (SA2) is currently investigating reference architecture models, concentrating on the network interfaces towards the WLAN. Group 3 (SA3) has now started work on security and authentication issues with regard to WLAN interworking . ETSI BRAN is currently liasing with the SA2 and SA3 groups. Internet Engineering Task Force (IETF) Within the recently created `eap' working group, extensions are being considered to EAP (mentioned in section 4), which will assist in system interworking. Institute of Electrical and Electronics Engineers (IEEE) USA The 802.11 WLAN technical groups are continuing to progress their family of standards. Many similarities exist between the current 802.11a standard and Hiperlan2/HiSWANa with regard to 3G interworking. ETSI BRAN is currently liasing with the Wireless Next Generation (WNG) group of the IEEE 802.11 project. Multimedia Mobile Access Communication (MMAC) Japan The High Speed Wireless Access (HSWA) group's HiSWANa (High Speed Wireless Access Network system A) is essentially identical to Hiperlan/2, except that it mandates the use of an Ethernet convergence layer within the access point. An agreement between ETSI BRAN and MMAC HSWA has now been in place for some time to share the output of the ETSI BRAN 3G interworking group. Conclusions This paper has addressed some of the current thinking within ETSI BRAN (and indeed WIG) regarding the interworking of the Hiperlan2 and HiSWANa wireless LAN systems into a 3G Cellular System. Much of this information is now appearing in the technical specification being jointly produced by ETSI and MMAC, expected to be published in the first half of 2003. Of the two initial solutions investigated (tight and loose coupling), current work has concentrated on the loose variant, producing viable solutions for security, mobility and QoS. The authentication schemes chosen will assume that EAP is carried over the air interface, thus being compatible, at the interworking level, with IEEE 802.11 and 3GPP. HIPERLAN/2 PUBLIC ACCESS INTERWORKING WITH 3G CELLULAR SYSTEMS 51 This standardisation activity thus hopes to ensure that all WLAN technologies can provide a value added service within hotspot environments for both customers and operators of 3G systems. Acknowledgements The authors wish to thank Maximilian Riegel (Siemens AG, Germany), Dr. Robert Hancock and Eleanor Hepworth (Roke Manor, UK) together with se Jevinger (Telia Research AB, Sweden) for their invaluable help and assistance with this work. References [1] ETSI TR 101 957 (V1.1.1): Broadband Radio Access Networks (BRAN); HIPERLAN Type 2; Requirements and Architectures for Interworking between Hiperlan/2 and 3rd Generation Cellular Systems (August 2001). [2] 3GPP TS 33.102: 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; 3G Security; Security Architecture . [3] L. Blunk, J. Vollbrecht and B. Aboba, PPP Extensible Authentication Protocol (EAP), RFC 2284bis, draft-ietf-pppext-rfc2284bis -04.txt (April 2002). [4] P. Calhoun et al., Diameter base protocol, draft-ietf-aaa-diameter -10 (April 2002). [5] C. Rigney et al., Remote Authentication Dial In User Service (RADIUS), RFC 2058 (January 1997). [6] HIPERLAN Type 2; Packet Based Convergence Layer; Part 2: Ethernet Service Specific Convergence Sublayer (SSCS), ETSI TS 101 493-2, BRAN. [7] HIPERLAN Type 2; System overview, ETSI TR 101 683, BRAN. [8] Information Technology Telecommunications and Information Exchange between Systems Local and Metropolitan Area Networks Common Specifications Part 3: Media Access Control (MAC) Bridges (Revision and redesignation of ISO/IEC 10038: 1993 [ANSI/IEEE Std 802.1D, 1993 Edition], incorporating IEEE supplements P802.1p, 802.1j-1996, 802.6k-1992, 802.11c-1998, and P802.12e)", ISO/IEC 15802-3: 1998. Stephen McCann holds a B.Sc. (Hons) degree from the University of Birmingham, England. He is currently editor of the ETSI BRAN "WLAN3G" interworking specification, having been involved in ETSI Hiperlan/2 standardisation for 3 years. He is also involved with both 802.11 work and that of the Japanese HiSWANa wireless LAN system. In the autumn of 2002, Stephen co-organised and attended the first WLAN Interworking Group (WIG) between ETSI BRAN, MMAC HSWA and IEEE 802.11. He is currently researching multimode WLAN/3G future terminals and WLAN systems for trains and ships, together with various satellite communications projects. In parallel to his Wireless LAN activities, Stephen has also been actively involved in the `rohc' working group of the IETF, looking at various Robust Header Compression schemes. Previously Stephen has been involved with avionics and was chief software integrator for the new Maastricht air traffic control system from 1995 to 1998. He is a chartered engineer and a member of the Institute of Electrical Engineers. E-mail: [email protected] Helena Flygare holds a M.Sc. degree in electrical engineering from Lund Institute of Technology, Sweden, where she also served as a teacher in Automatic Control for the Master Degree program. Before her present job she worked in various roles with system design for hardware and software development . In 1999 she joined Radio System Malm at Telia Research AB. She works with specification, design and integration between systems with different access technologies, e.g. WLANs, 2.5/3G, etc. from a technical, as well as from a business perspective. Since the year 2000, she has been active with WLAN interworking with 3G and other public access networks in HiperLAN/2 Global Forum, ETSI/BRAN, and 3GPP. E-mail: [email protected]

Hiperlan/2;interworking;3G;ETSI;BRAN;WIG;public access

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2D Information Displays

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"INTRODUCTION\nIn many areas knowledge about structures and their meaning\nas well as their spatial (...TRUNCATED)

Information visualization;Spreading activation

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Impedance Coupling in Content-targeted Advertising

"The current boom of the Web is associated with the revenues originated from on-line advertising. Wh(...TRUNCATED)

"INTRODUCTION\nThe emergence of the Internet has opened up new marketing\nopportunities. In fact, a (...TRUNCATED)

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Implementing the IT Fundamentals Knowledge Area

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IT Fundamentals Knowledge Area;IT Model Curriculum

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Implicit User Modeling for Personalized Search

"Information retrieval systems (e.g., web search engines) are critical for overcoming information ov(...TRUNCATED)

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"user model;interactive retrieval;personalized search;information retrieval systems;user modelling;i(...TRUNCATED)

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Improvements of TLAESA Nearest Neighbour Search Algorithm and Extension to Approximation Search

"Nearest neighbour (NN) searches and k nearest neighbour (k-NN) searches are widely used in pattern (...TRUNCATED)

"Introduction\nNN and k-NN searches are techniques which find the\nclosest object (closest k objects(...TRUNCATED)

"Approximation Search;TLAESA;Distance Computaion;k Nearest Neighbour Search;Nearest Neighbour Search(...TRUNCATED)

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Improving the Static Analysis of Embedded Languages via Partial Evaluation

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"1. One Language, Many Languages\nEvery practical programming language contains small programming\nl(...TRUNCATED)

"macros;interpreter;value flow analysis;flow analysis;set-based analysis;partial evaluation;embedded(...TRUNCATED)