We may enforce an information flow policy by encrypting a protected resource and ensuring that only users authorized by the policy are able to decrypt the resource. In most schemes in the literature that use symmetric cryptographic primitives, each user is assigned a single secret and derives decryption keys using this secret and publicly available information. Recent work has challenged this approach by developing schemes, based on a chain partition of the information flow policy, that do not require public information for key derivation, the trade-off being that a user may need to be assigned more than one secret. In general, many different chain partitions exist for the same policy and, until now, it was not known how to compute an appropriate one. In this paper, we introduce the notion of a tree partition, of which chain partitions are a special case. We show how a tree partition may be used to define a cryptographic enforcement scheme and prove that such schemes can be instantiated in such a way as to preserve the strongest security properties known for cryptographic enforcement schemes. We establish a number of results linking the amount of secret material that needs to be distributed to users with a weighted acyclic graph derived from the tree partition. These results enable us to develop efficient algorithms for deriving tree and chain partitions that minimize the amount of secret material that needs to be distributed.
The significant open problem with prior work on chain-based schemes is the assumption that the chain partition is part of the input to the algorithm: there may be many such partitions and it is not immediately obvious how one should select a specific partition in order to optimize characteristics of the corresponding enforcement scheme (an example being to minimize the number of secrets issued). Hence, it seems very natural to ask how difficult it is to compute a good'' chain partition, given that Our recent work @cite_2 shows that it is possible to compute a minimal chain partition in polynomial time using a minimum cost network flow algorithm.
@cite_2
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The simple security property in an information flow policy can be enforced by encrypting data objects and distributing an appropriate secret to each user. A user derives a suitable decryption key from the secret and publicly available information. A chain-based enforcement scheme provides an alternative method of cryptographic enforcement that does not require any public information, the trade-off being that a user may require more than one secret. For a given information flow policy, there will be many different possible chain-based enforcement schemes. In this paper, we provide a polynomial-time algorithm for selecting a chain-based scheme which uses the minimum possible number of secrets. We also compute the number of secrets that will be required and establish an upper bound on the number of secrets required by any user. We present a model for video segmentation, applicable to RGB (and if available RGB-D) information that constructs multiple plausible partitions corresponding to the static and the moving objects in the scene: i) we generate multiple figure-ground segmentations, in each frame, parametrically, based on boundary and optical flow cues, then track, link and refine the salient segment chains corresponding to the different objects, over time, using long-range temporal constraints, ii) a video partition is obtained by composing segment chains into consistent tilings, where the different individual object chains explain the video and do not overlap. Saliency metrics based on figural and motion cues, as well as measures learned from human eye movements are exploited, with substantial gain, at the level of segment generation and chain construction, in order to produce compact sets of hypotheses which correctly reflect the qualities of the different configurations. The model makes it possible to compute multiple hypotheses over both individual object segmentations tracked over time, and for complete video partitions. We report quantitative, state of the art results in the SegTrack single object benchmark, and promising qualitative and quantitative results in clips filming multiple static and moving objects collected from Hollywood movies and from the MIT dataset. A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs, and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of an arbitrary JDM, realizations in which the links between any two fixed-degree groups of nodes are placed as uniformly as possible. We prove that a swap Markov chain Monte Carlo algorithm in the space of all balanced realizations of an arbitrary graphical JDM mixes rapidly, i.e., the relaxation time of the chain is bounded from above by a polynomial in the number of nodes @math . To prove fast mixing, we first prove a general factorization theorem similar to the Martin--Randall method for disjoint decompositions (partitions). This theorem can be used to bound from below the spectral gap with the help of fast mixing subchains within every partition and a bound on an auxiliary Markov chain between the partitions. Our proof of the general factorization theorem is direct and ... Parallel Matrix-Matrix Multiplication (MMM) is a fundamental part of the linear algebra libraries used by scientific applications on high performance computers. As heterogeneous systems have emerged as high performance computing platforms, the traditional homogeneous algorithms have been adapted to these heterogeneous environments. Although heterogeneous systems have been in use for some time, it remains an open problem of how to optimally partition data on heterogeneous processors to minimize computation, communication, and execution time. While the question of how to subdivide these MMM problems among heterogeneous processors has been studied, the underlying assumption of this prior study is that the data partition shape, the layout of the data within the matrix assigned to each processor, should be rectangular, i.e. that each processor should be assigned a rectangular portion of the matrix to compute. Our previous work in this area questioned the optimality of this traditional rectangular shape and studied this partition shape problem for two processors. In that work, we proposed a novel mathematical method for transforming partition shapes to decrease communication cost and an analytical technique for determining the optimal shape. In this work, we extend this technique to apply to three and more heterogeneous processors. While applying this method to two processors is relatively straightforward, the complexity grows immensely when considering three processors. With this complexity in mind, we propose a hybrid of experimental and analytical techniques. We postulate that a small number of partition shapes are potentially optimal, and perform extensive testing using a computer aided method to apply our previously developed analytical technique, without finding a counterexample. We identified six data partition shapes which are candidates to be the optimal three processor shape. In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is existentially optimal) establishes an important analogue of the famous 1-commodity max-flow min-cut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper. Categories and Subject Descriptors: F.2.2 (Analysis of Algorithms and Problem Complexity): This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notion of asymptotically level stable (als) functions, we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of multipliers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method. Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering. In this paper we consider the problem of (k, υ)-balanced graph partitioning - dividing the vertices of a graph into k almost equal size components (each of size less than υ • n k) so that the capacity of edges between different components is minimized. This problem is a natural generalization of several other problems such as minimum bisection, which is the (2,1)-balanced partitioning problem. We present a bicriteria polynomial time approximation algorithm with an O(log2n)-approximation for any constant υ > 1. For υ = 1 we show that no polytime approximation algorithm can guarantee a finite approximation ratio unless P=NP. Previous work has only considered the (k, υ)-balanced partitioning problem for υ ≥ 2. Vision tasks, such as segmentation, grouping, recognition, can be formulated as graph partition problems. The recent literature witnessed two popular graph cut algorithms: the Ncut using spectral graph analysis and the minimum-cut using the maximum flow algorithm. We present a third major approach by generalizing the Swendsen-Wang method - a well celebrated algorithm in statistical mechanics. Our algorithm simulates ergodic, reversible Markov chain jumps in the space of graph partitions to sample a posterior probability. At each step, the algorithm splits, merges, or regroups a sizable subgraph, and achieves fast mixing at low temperature enabling a fast annealing procedure. Experiments show it converges in 2-30 seconds on a PC for image segmentation. This is 400 times faster than the single-site update Gibbs sampler, and 20-40 times faster than the DDMCMC algorithm. The algorithm can optimize over the number of models and works for general forms of posterior probabilities, so it is more general than the existing graph cut approaches. The paper is concerned with tools for the quantitative analysis of finite Markov chains whose states are combinatorial structures. Chains of this kind have algorithmic applications in many areas, including random sampling, approximate counting, statistical physics and combinatorial optimisation. The efficiency of the resulting algorithms depends crucially on the mixing rate of the chain, i.e. , the time taken for it to reach its stationary or equilibrium distribution. The paper presents a new upper bound on the mixing rate, based on the solution to a multicommodity flow problem in the Markov chain viewed as a graph. The bound gives sharper estimates for the mixing rate of several important complex Markov chains. As a result, improved bounds are obtained for the runtimes of randomised approximation algorithms for various problems, including computing the permanent of a 0–1 matrix, counting matchings in graphs, and computing the partition function of a ferromagnetic Ising system. Moreover, solutions to the multicommodity flow problem are shown to capture the mixing rate quite closely: thus, under fairly general conditions, a Markov chain is rapidly mixing if and only if it supports a flow of low cost. Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. of the 6th SIAM Conference on Parallel Processing for Scientific Computing, 1993, 445--452; Hendrickson and Leland, A Multilevel Algorithm for Partitioning Graphs, Tech. report SAND 93-1301, Sandia National Laboratories, Albuquerque, NM, 1993]. From the early work it was clear that multilevel techniques held great promise; however, it was not known if they can be made to consistently produce high quality partitions for graphs arising in a wide range of application domains. We investigate the effectiveness of many different choices for all three phases: coarsening, partition of the coarsest graph, and refinement. In particular, we present a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of the size of the final partition obtained after multilevel refinement. We also present a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening. We test our scheme on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation. Our experiments show that our scheme produces partitions that are consistently better than those produced by spectral partitioning schemes in substantially smaller time. Also, when our scheme is used to compute fill-reducing orderings for sparse matrices, it produces orderings that have substantially smaller fill than the widely used multiple minimum degree algorithm. The SDN and NFV paradigms enable novel network services which can be realized and embedded in a flexible and rapid manner. For example, SDN can be used to flexibly steer traffic from a source to a destination through a sequence of virtualized middleboxes, in order to realize so-called service chains. The service chain embedding problem consists of three tasks: admission control, finding suitable locations to allocate the virtualized middleboxes and computing corresponding routing paths. This paper considers the offline batch embedding of multiple service chains. Concretely, we consider the objectives of maximizing the profit by embedding an optimal subset of requests or minimizing the costs when all requests need to be embedded. Interestingly, while the service chain embedding problem has recently received much attention, so far, only non- polynomial time algorithms (based on integer programming) as well as heuristics (which do not provide any formal guarantees) are known. This paper presents the first polynomial time service chain approximation algorithms both for the case with admission and without admission control. Our algorithm is based on a novel extension of the classic linear programming and randomized rounding technique, which may be of independent interest. In particular, we show that our approach can also be extended to more complex service graphs, containing cycles or sub-chains, hence also providing new insights into the classic virtual network embedding problem. Parallel database systems horizontally partition large amounts of structured data in order to provide parallel data processing capabilities for analytical workloads in shared-nothing clusters. One major challenge when horizontally partitioning large amounts of data is to reduce the network costs for a given workload and a database schema. A common technique to reduce the network costs in parallel database systems is to co-partition tables on their join key in order to avoid expensive remote join operations. However, existing partitioning schemes are limited in that respect since only subsets of tables in complex schemata sharing the same join key can be co-partitioned unless tables are fully replicated. In this paper we present a novel partitioning scheme called predicate-based reference partition (or PREF for short) that allows to co-partition sets of tables based on given join predicates. Moreover, based on PREF, we present two automatic partitioning design algorithms to maximize data-locality. One algorithm only needs the schema and data whereas the other algorithm additionally takes the workload as input. In our experiments we show that our automated design algorithms can partition database schemata of different complexity and thus help to effectively reduce the runtime of queries under a given workload when compared to existing partitioning approaches. We analyze and solve a game in which a player chooses which of several Markov chains to advance, with the object of minimizing the expected time (or cost) for one of the chains to reach a target state. The solution entails computing (in polynomial time) a function @math ---a variety of "Gittins index"---on the states of the individual chains, the minimization of which produces an optimal strategy. It turns out that @math is a useful cousin of the expected hitting time of a Markov chain but is defined, for example, even for random walks on infinite graphs. We derive the basic properties of @math and consider its values in some natural situations. Network function (NF) virtualization decouples NFs from the underlying middlebox hardware and promotes their deployment on virtualized network infrastructures. This essentially paves the way for the migration of NFs into clouds (i.e., NF-as-a-Service), achieving a drastic reduction of middlebox investment and operational costs for enterprises. In this context, service chains (expressing middlebox policies in the enterprise network) should be mapped onto datacenter networks, ensuring correctness, resource efficiency, as well as compliance with the provider’s policy. The network service embedding (NSE) problem is further exacerbated by two challenging aspects: 1) traffic scaling caused by certain NFs (e.g., caches and WAN optimizers) and 2) NF location dependencies. Traffic scaling requires resource reservations different from the ones specified in the service chain, whereas NF location dependencies, in conjunction with the limited geographic footprint of NF providers (NFPs), raise the need for NSE across multiple NFPs. In this paper, we present a holistic solution to the multi-provider NSE problem. We decompose NSE into: 1) NF-graph partitioning performed by a centralized coordinator and 2) NF-subgraph mapping onto datacenter networks. We present linear programming formulations to derive near-optimal solutions for both problems. We address the challenging aspect of traffic scaling by introducing a new service model that supports demand transformations. We also define topology abstractions for NF-graph partitioning. Furthermore, we discuss the steps required to embed service chains across multiple NFPs, using our NSE orchestrator (Nestor). We perform an evaluation study of multi-provider NSE with emphasis on NF-graph partitioning optimizations tailored to the client and NFPs. Our evaluation results further uncover significant savings in terms of service cost and resource consumption due to the demand transformations. Partitioning large graphs is difficult, especially when performed in the limited models of computation afforded to modern large scale computing systems. In this work we introduce restreaming graph partitioning and develop algorithms that scale similarly to streaming partitioning algorithms yet empirically perform as well as fully offline algorithms. In streaming partitioning, graphs are partitioned serially in a single pass. Restreaming partitioning is motivated by scenarios where approximately the same dataset is routinely streamed, making it possible to transform streaming partitioning algorithms into an iterative procedure. This combination of simplicity and powerful performance allows restreaming algorithms to be easily adapted to efficiently tackle more challenging partitioning objectives. In particular, we consider the problem of stratified graph partitioning, where each of many node attribute strata are balanced simultaneously. As such, stratified partitioning is well suited for the study of network effects on social networks, where it is desirable to isolate disjoint dense subgraphs with representative user demographics. To demonstrate, we partition a large social network such that each partition exhibits the same degree distribution in the original graph --- a novel achievement for non-regular graphs. As part of our results, we also observe a fundamental difference in the ease with which social graphs are partitioned when compared to web graphs. Namely, the modular structure of web graphs appears to motivate full offline optimization, whereas the locally dense structure of social graphs precludes significant gains from global manipulations. In this paper we present a parallel formulation of the multilevel graph partitioning and sparse matrix ordering algorithm. A key feature of our parallel formulation (that distinguishes it from other proposed parallel formulations of multilevel algorithms) is that it partitions the vertices of the graph intopparts while distributing the overall adjacency matrix of the graph among allpprocessors. This mapping results in substantially smaller communication than one-dimensional distribution for graphs with relatively high degree, especially if the graph is randomly distributed among the processors. We also present a parallel algorithm for computing a minimal cover of a bipartite graph which is a key operation for obtaining a small vertex separator that is useful for computing the fill reducing ordering of sparse matrices. Our parallel algorithm achieves a speedup of up to 56 on 128 processors for moderate size problems, further reducing the already moderate serial run time of multilevel schemes. Furthermore, the quality of the produced partitions and orderings are comparable to those produced by the serial multilevel algorithm that has been shown to outperform both spectral partitioning and multiple minimum degree. Although collision free TDMA schemes have been proposed and used for more than two decades, an important ingredient of these schemes, the initialization of stations (that is, assigning ID numbers 1,2,...,n) was not investigated until recently. Binary and n-ary partitioning algorithms were recently proposed for the case of stations with collision detection capability. The main contribution of this paper is a new randomized hybrid initialization protocol which combines the two partitioning algorithms into a more efficient one. The new scheme optimizes the binary partition protocol for small values of n (e.g. n=2, 3, 4). The hybrid scheme then applies n-ary partition protocol on the whole set, followed by binary partition on the stations that caused collision. We proved analytically that the expected number of time slots in the hybrid algorithm with known number of users is <2.20? n. Performance of these algorithms was also evaluated experimentally by comparing it with existing algorithms, and an improvement from e? n to approximately 2.15? n was obtained. We consider the problem of partitioning the nodes of a graph with costs on its edges into subsets of given sizes so as to minimize the sum of the costs on all edges cut. This problem arises in several physical situations — for example, in assigning the components of electronic circuits to circuit boards to minimize the number of connections between boards. This paper presents a heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems. In recent years, Massively Parallel Processors (MPPs) have gained ground enabling vast amounts of data processing. In such environments, data is partitioned across multiple compute nodes, which results in dramatic performance improvements during parallel query execution. To evaluate certain relational operators in a query correctly, data sometimes needs to be re-partitioned (i.e., moved) across compute nodes. Since data movement operations are much more expensive than relational operations, it is crucial to design a suitable data partitioning strategy that minimizes the cost of such expensive data transfers. A good partitioning strategy strongly depends on how the parallel system would be used. In this paper we present a partitioning advisor that recommends the best partitioning design for an expected workload. Our tool recommends which tables should be replicated (i.e., copied into every compute node) and which ones should be distributed according to specific column(s) so that the cost of evaluating similar workloads is minimized. In contrast to previous work, our techniques are deeply integrated with the underlying parallel query optimizer, which results in more accurate recommendations in a shorter amount of time. Our experimental evaluation using a real MPP system, Microsoft SQL Server 2008 Parallel Data Warehouse, with both real and synthetic workloads shows the effectiveness of the proposed techniques and the importance of deep integration of the partitioning advisor with the underlying query optimizer.