2320085
Generating random regular graphs
Random regular graphs play a central role in combinatorics and theoretical computer science. In this paper, we analyze a simple algorithm introduced by Steger and Wormald [9] and prove that it produces an asymptotically uniform random regular graph in a polynomial time. Precisely, for fixed d and n with d=O(n1/3-ε), it is shown that the algorithm generates an asymptotically uniform random d-regular graph on n vertices in time O(nd2). This confirms a conjecture of Wormald. The key ingredient in the proof is a recently developed concentration inequality by the second author.Besides being perhaps the only algorithm which works for relatively large d in practical time, our result also has a significant theoretical value, as it can be used to derive many properties of uniform random regular graphs.
18028546
Divide and conquer martingales and the number of triangles in a random graph
The goal of this paper is to present a novel application of a recent and useful martingale inequality. As an illustration, we prove an essentially sharp bound for the probability that a random graph contains significantly more triangles than expected.
3103350
Random Matchings in Regular Graphs
d-regular graph G, let M be chosen uniformly at random from the set of all matchings of G, and for let be the probability that M does not cover x.We show that for large d, the 's and the mean μ and variance of are determined to within small tolerances just by d and (in the case of μ and ) :
Theorem. For any d-regular graph G,
(a), so that ,
(b),where the rates of convergence depend only on d.
11005224
A phase transition for avoiding a giant component
Let c be a constant and (e1, f1), (e2, f2), . . . , (ecn, fcn) be a sequence of ordered pairs of edges from the complete graph Kn chosen uniformly and independently at random. We prove that there exists a constant c2 such that if c > c2 then whp every graph which contains at least one edge from each ordered pair (ei, fi) has a component of size Ω(n) and if c < c2 then whp there is a graph containing at least one edge from each pair that has no component with more than O ( n1−2 ) vertices, where 2 is a constant that depends on c2− c. The constant c2 is roughly 0.97677.
14012710
Interference-Minimizing Colorings of Regular Graphs
Communications problems that involve frequency interference, such as the channel assignment problem in the design of cellular telephone networks, can be cast as graph coloring problems in which the frequencies (colors) assigned to an edge's vertices interfere if they are too similar. The paper considers situations modeled by vertex-coloring d-regular graphs with n vertices using a color set 1, 2,..., n, where colors i and j are said to interfere if their circular distance $\min \{ | i-j | , n- | i-j | \}$ does not exceed a given threshold value $\alpha$. Given a d-regular graph G and threshold $\alpha$, an interference-minimizing coloring is a coloring of vertices that minimizes the number of edges that interfere. Let $I_\alpha (G)$ denote the minimum number of interfering edges in such a coloring of $G$. For most triples $(n, \alpha ,d),$ we determine the minimum value of $I_\alpha (G)$ over all d-regular graphs and find graphs that attain it. In determining when this minimum value is 0, we prove that for $r \geq 3$ there exists a d-regular graph G on n vertices that is r-colorable whenever $d \leq (1- \frac{1}{r}) n-1$ and nd is even. We also study the maximum value of $I_\alpha (G)$ over all d-regular graphs and find graphs that attain this maximum in many cases.
12050804
On the asymmetry of random regular graphs and random graphs
This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n - 4 the random d-regular graph on n vertices almost surely has no nontrivial automorphisms. This answers an open question of N. Wormald [13].
12043862
A method and tool support for variant requirements analysis: goal and scenario based approach
Identifying and representing variant requirements among products in a product family are crucial activities for a successful software reuse. The variant requirements should be not only identified based on the business goal, which drives marketing plan, product plan, and differences among products, but also represented as familiar notations in order to support developing a particular product in the product family. Thus, our proposal is to identify the variant requirements through goals and scenarios, and represent them as variable use cases for a product family. Especially, for identification of the variant requirements, we propose four abstraction levels of requirements in the product family, and goal and scenario modeling. For representation of them, variable use case model is suggested, and also the use case transfer rules are proposed so as to bridge the gap between the identification and representation activity. The paper illustrates the application of the approach within a supporting tool, namely DREAM (Domain REquirements Analysis Method) using the ATM example.
14673300
A Polynomial Time Approximation Scheme for the Problem of Interconnecting Highways
AbstractThe objective of the Interconnecting Highways problem is to construct roads of minimum total length to interconnect n given highways under the constraint that the roads can intersect each highway only at one point in a designated interval which is a line segment. We present a polynomial time approximation scheme for this problem by applying Arora's framework (Arora, 1998; also available from http:www.cs.princeton.edu/~arora). For every fixed c > 1 and given any n line segments in the plane, a randomized version of the scheme finds a 
$$\left( {1 + \frac{1}{c}} \right)$$
-approximation to the optimal cost in O(nO(c)log(n) time.
1994375
Effective Temporal Aggregation Using Point-Based Trees
Temporal databases introduce the concept of time into underlying data, and provide built-in facilities that allow users to store and retrieve time-varying data. The aggregation in temporal databases, that is, temporal aggregation is an extension of conventional aggregation on the domain and range of aggregates to include time concept. Temporal aggregation is important for various applications, but is very expensive. In this paper, we propose a new tree structure for temporal aggregation, called PA-tree, and aggregate processing method based on the PA-tree. We show that the time complexity of the proposed method is better than those of the existing methods. The time complexity of the proposed method is shown to be indeed the lower bound of the problem. We perform comparative experiments and show the performance advantage of our proposed method in practice.
68452
Danger Theory: The Link between AIS and IDS?
We present ideas about creating a next generation Intrusion Detection System (IDS) based on the latest immunological theories. The central challenge with computer security is determining the difference between normal and potentially harmful activity. For half a century, developers have protected their systems by coding rules that identify and block specific events. However, the nature of current and future threats in conjunction with ever larger IT systems urgently requires the development of automated and adaptive defensive tools. A promising solution is emerging in the form of Artificial Immune Systems (AIS): The Human Immune System (HIS) can detect and defend against harmful and previously unseen invaders, so can we not build a similar Intrusion Detection System (IDS) for our computers? Presumably, those systems would then have the same beneficial properties as HIS like error tolerance, adaptation and self-monitoring. Current AIS have been successful on test systems, but the algorithms rely on self-nonself discrimination, as stipulated in classical immunology. However, immunologist are increasingly finding fault with traditional self-nonself thinking and a new ‘Danger Theory’ (DT) is emerging. This new theory suggests that the immune system reacts to threats based on the correlation of various (danger) signals and it provides a method of ‘grounding’ the immune response, i.e. linking it directly to the attacker. Little is currently understood of the precise nature and correlation of these signals and the theory is a topic of hot debate. It is the aim of this research to investigate this correlation and to translate the DT into the realms of computer security, thereby creating AIS that are no longer limited by self-nonself discrimination. It should be noted that we do not intend to defend this controversial theory per se, although as a deliverable this project will add to the body of knowledge in this area. Rather we are interested in its merits for scaling up AIS applications by overcoming self-nonself discrimination problems.
15453065
Device-Aware Cache Replacement Algorithm for Heterogeneous Mobile Storage Devices
Hard disks, most prevalent mass-storage devices, have high power consumption and high response time for random I/O requests. Recent remarkable technology improvement of flash memory has made it a rising secondary storage device but flash memory still has high cost per bit. Usage of heterogeneous storage devices such as a pair of a hard disk and a flash memory can provide reasonable cost, relatively acceptable response time, and low-power consumption. In this paper, we propose a novel buffer cache replacement algorithm which targets a mobile computing system with a heterogeneous storage pair of a hard disk and a flash memory. The algorithm partitions the cache per each device and adjusts the size of each partition based on the performance indices of the devices, and manages each partition according to workload patterns. Simulations show that the proposed algorithm yields a hit rate up to two times higher than LRU on the typical mobile traces according to the cache size and achieves also better system I/O response time and energy consumption.