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15
A Randomized Fully Polynomial Time Approximation Scheme for the All Terminal Network Reliability Problem
, 1997
"... The classic allterminal network reliability problem posits a graph, each of whose edges fails (disappears) independently with some given probability. The goal is to determine the probability that the network becomes disconnected due to edge failures. The practical applications of this question to c ..."
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Cited by 76 (2 self)
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The classic allterminal network reliability problem posits a graph, each of whose edges fails (disappears) independently with some given probability. The goal is to determine the probability that the network becomes disconnected due to edge failures. The practical applications of this question to communication networks are obvious, and the problem hasthereforebeenthesubjectofagreatdealofstudy. Sinceitis]Pcomplete, andthusbelievedhardtosolveexactly, a great deal of researchhasbeendevotedtoestimatingthefailureprobability. Acomprehensivesurveycanbefoundin[Col87]. Therstauthorrecentlypresentedanalgorithmfor approximatingtheprobabilityofnetworkdisconnection underrandomedgefailures. In this paper, we report onourexperienceimplementingthisalgorithm.Our implementationshowsthatthealgorithmispractical onnetworksofmoderatesize, and indeedworksbetter thanthetheoreticalboundspredict. Part of this improvementarisesfromheuristicmodicationstothe theoreticalalgorithm, whileanotherpartsuggests that thetheoreticalrunningtimeanalysisofthealgorithm might not be tight. Based on our observation of the implementation, wewereabletodeviseanalyticexplanationsofatleast someoftheimprovedperformance. As one example, we formallyprovetheaccuracyofasimpleheuristic approximationforthereliability. Wealsodiscussother questionsraisedbytheimplementationwhichmightbe susceptibletoanalysis.
An Optimal Algorithm for Monte Carlo Estimation
, 1995
"... A typical approach to estimate an unknown quantity is to design an experiment that produces a random variable Z distributed in [0; 1] with E[Z] = , run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a ..."
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Cited by 61 (4 self)
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A typical approach to estimate an unknown quantity is to design an experiment that produces a random variable Z distributed in [0; 1] with E[Z] = , run this experiment independently a number of times and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is distributed in [0; 1]. We describe an approximation algorithm AA which, given ffl and ffi, when running independent experiments with respect to any Z, produces an estimate that is within a factor 1 + ffl of with probability at least 1 \Gamma ffi. We prove that the expected number of experiments run by AA (which depends on Z) is optimal to within a constant factor for every Z. An announcement of these results appears in P. Dagum, D. Karp, M. Luby, S. Ross, "An optimal algorithm for MonteCarlo Estimation (extended abstract)", Proceedings of the Thirtysixth IEEE Symposium on Foundations of Computer Science, 1995, pp. 142149 [3]. Section ...
Monte Carlo Model Checking
 In Proc. of Tools and Algorithms for Construction and Analysis of Systems (TACAS 2005), volume 3440 of LNCS
, 2005
"... Abstract. We present MC 2, what we believe to be the first randomized, Monte Carlo algorithm for temporallogic model checking, the classical problem of deciding whether or not a property specified in temporal logic holds of a system specification. Given a specification S of a finitestate system, a ..."
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Cited by 55 (4 self)
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Abstract. We present MC 2, what we believe to be the first randomized, Monte Carlo algorithm for temporallogic model checking, the classical problem of deciding whether or not a property specified in temporal logic holds of a system specification. Given a specification S of a finitestate system, an LTL (Linear Temporal Logic) formula ϕ, and parameters ɛ and δ, MC 2 takes N = ln(δ) / ln(1 − ɛ) random samples (random walks ending in a cycle, i.e lassos) from the Büchi automaton B = BS × B¬ϕ to decide if L(B) = ∅. Should a sample reveal an accepting lasso l, MC 2 returns false with l as a witness. Otherwise, it returns true and reports that with probability less than δ, pZ < ɛ, where pZ is the expectation of an accepting lasso in B. It does so in time O(N · D) and space O(D), where D is B’s recurrence diameter, using a number of samples N that is optimal to within a constant factor. Our experimental results demonstrate that MC 2 is fast, memoryefficient, and scales very well.
An introduction to randomized algorithms
 Discrete Appl Math
, 1991
"... Research conducted over the past fifteen years has amply demonstrated the advantages of algorithms that make random choices in the course of their execution. This paper presents a wide variety of examples intended to illustrate the range of applications of randomized algorithms, and the general prin ..."
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Cited by 34 (0 self)
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Research conducted over the past fifteen years has amply demonstrated the advantages of algorithms that make random choices in the course of their execution. This paper presents a wide variety of examples intended to illustrate the range of applications of randomized algorithms, and the general principles and approaches that are of greatest use in their construction. The examples are drawn from many areas, including number theory, algebra, graph theory, pattern matching, selection, sorting, searching, computational geometry, combinatorial enumeration, and parallel and distributed computation. 1. Foreword This paper is derived from a series of three lectures on randomized algorithms presented by the author at a conference on combinatorial mathematics and algorithms held at George Washington University in May, 1989. The purpose of the paper is to convey, through carefully selected examples, an understanding of the nature of randomized algorithms, the range of their applications and the principles underlying their construction. It is not our goal to be encyclopedic, and thus the paper should not be regarded as a comprehensive survey of the subject. This paper would not have come into existence without the magnificent efforts of Professor Rodica Simion, the organizer of the conference at George Washington University. Working from the taperecorded lectures, she created a splendid transcript that served as the first draft of the paper. Were it not for her own reluctance she would be listed as my coauthor.
Reliability in Layered Networks with Random Link Failures
"... Abstract—We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the ..."
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Abstract—We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multilayer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low failure probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability. I.
A deterministic polynomialtime approximation scheme for counting knapsack solutions
, 1008
"... Abstract. Given n elements with nonnegative integer weights w1,...,wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given capacity. We give a deterministic algorithm that estimates ..."
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Cited by 6 (0 self)
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Abstract. Given n elements with nonnegative integer weights w1,...,wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given capacity. We give a deterministic algorithm that estimates the number of solutions to within relative error 1±ε in time polynomial in n and 1/ε (fully polynomial approximation scheme). More precisely, our algorithm takes time O(n3ε−1 log(n/ε)). Our algorithm is based on dynamic programming. Previously, randomized polynomialtime approximation schemes were known first by Morris and Sinclair via Markov chain Monte Carlo techniques and subsequently by Dyer via dynamic programming and rejection sampling. Key words. approximate counting, knapsack, dynamic programming 1. Introduction. Randomized
An FPTAS for #Knapsack and Related Counting Problems
"... Given n elements with nonnegative integer weights w1,...,wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most C. We give the first deterministic, fully polynomialtime approximation scheme ..."
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Cited by 4 (1 self)
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Given n elements with nonnegative integer weights w1,...,wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most C. We give the first deterministic, fully polynomialtime approximation scheme (FPTAS) for estimating the number of solutions to any knapsack constraint (our estimate has relative error 1 ± ε). Our algorithm is based on dynamic programming. Previously, randomized polynomialtime approximation schemes (FPRAS) were known first by Morris and Sinclair via Markov chain Monte Carlo techniques, and subsequently by Dyer via dynamic programming and rejection sampling. In addition, we present a new method for deterministic approximate counting using readonce branching programs. Our approach yields an FPTAS for several other counting problems, including counting solutions for the multidimensional knapsack problem with a constant number of constraints, the general integer knapsack problem, and the contingency tables problem with a constant number of rows.
Modeling and Analysis of the Collective Dynamics of LargeScale MultiAgent Systems: A Cellular and Network Automata based Approach
, 2006
"... This technical report addresses a particular approach to modeling and analysis of the behavior of largescale multiagent systems. A broad variety of multiagent systems are modeled as appropriate variants of cellular and network automata. Several fundamental properties of the collective dynamics of ..."
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Cited by 2 (0 self)
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This technical report addresses a particular approach to modeling and analysis of the behavior of largescale multiagent systems. A broad variety of multiagent systems are modeled as appropriate variants of cellular and network automata. Several fundamental properties of the collective dynamics of those cellular and network automata are then formally analyzed. Various loosely coupled largescale distributed information systems are of an increasing interest in a variety of areas of computer science and its applications – areas as diverse as team robotics, intelligent transportation systems, open distributed software environments, disaster response management, distributed databases and information retrieval, and computational theories of language evolution. A popular paradigm for abstracting such distributed infrastructures is that of multiagent systems (MAS) made of typically a large number of autonomous agents that locally interact with each other. This report is an attempt at a cellular and network automata based mathematical and computational theory of such MAS. The