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30
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
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Cited by 161 (0 self)
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 114 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
Computing the Types of Relationships Between Autonomous Systems
 in Proceedings of IEEE Infocom
, 2003
"... Abstract — We investigate the problem of computing the types of the relationships between Internet Autonomous Systems. We refer to the model introduced in [1], [2] that bases the discovery of such relationships on the analysis of the AS paths extracted from the BGP routing tables. We characterize th ..."
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Cited by 49 (0 self)
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Abstract — We investigate the problem of computing the types of the relationships between Internet Autonomous Systems. We refer to the model introduced in [1], [2] that bases the discovery of such relationships on the analysis of the AS paths extracted from the BGP routing tables. We characterize the time complexity of the above problem, showing both NPcompleteness results and efficient algorithms for solving specific cases. Motivated by the hardness of the general problem, we propose heuristics based on a novel paradigm and show their effectiveness against publicly available data sets. The experiments put in evidence that our heuristics performs significantly better than state of the art heuristics. I.
Intelligent Backtracking On Constraint Satisfaction Problems: Experimental And Theoretical Results
, 1995
"... The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which ess ..."
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Cited by 47 (0 self)
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The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependencydirected backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronologica...
Computing the Types of the Relationships between Autonomous Systems
 in Proc. IEEE INFOCOM
, 2003
"... We investigate the problem of computing the types of the relationships between Internet Autonomous Systems. We refer to the model introduced in [1], [2] that bases the discovery of such relationships on the analysis of the AS paths extracted from the BGP routing tables. We characterize the time comp ..."
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Cited by 46 (8 self)
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We investigate the problem of computing the types of the relationships between Internet Autonomous Systems. We refer to the model introduced in [1], [2] that bases the discovery of such relationships on the analysis of the AS paths extracted from the BGP routing tables. We characterize the time complexity of the above problem, showing both NPcompleteness results and efficient algorithms for solving specific cases. Motivated by the hardness of the general problem, we propose heuristics based on a novel paradigm and show their effectiveness against publicly available data sets. The experiments put in evidence that our heuristics performs significantly better than state of the art heuristics.
Threshold Phenomena in Random Graph Colouring and Satisfiability
, 1999
"... We study threshold phenomena pertaining to the colourability of random graphs and the satisfiability of random formulas. Consider a random graph G(n, p) on n vertices formed by including each of the possible edges independently of all others with probability p. For a fixed integer k, let f k ..."
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Cited by 24 (4 self)
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We study threshold phenomena pertaining to the colourability of random graphs and the satisfiability of random formulas. Consider a random graph G(n, p) on n vertices formed by including each of the possible edges independently of all others with probability p. For a fixed integer k, let f k (n, d) = Pr[G(n, d/n) is kcolourable]. Erdos asked the following fundamental question: for k 3, is there a constant c k such that for any # > 0, #) = 1 , and lim f k (n, c k + #) = 0 ? (1) We prove that for all k 3, there exists a function t k (n) such that (1) holds upon replacing c k by t k (n), thus establishing that indeed kcolourability has a sharp threshold. Let d k = sup{d lim n## f k (n, d) = 1}. Note that if c k exists then, by definition, c k = d k . For the basic and most studied case k = 3 we prove 3.84 < d 3 < 5.05 . These are the best
The computational complexity of quantified constraint satisfaction
, 2004
"... The constraint satisfaction problem (CSP) is a framework for modelling search problems. An instance of the CSP consists of a set of variables and a set of constraints on the variables; the question is to decide whether or not there is an assignment to the variables satisfying all of the constraints. ..."
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Cited by 20 (8 self)
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The constraint satisfaction problem (CSP) is a framework for modelling search problems. An instance of the CSP consists of a set of variables and a set of constraints on the variables; the question is to decide whether or not there is an assignment to the variables satisfying all of the constraints. The quantified constraint satisfaction problem (QCSP) is a generalization of the CSP in which variables may be both universally and existentially quantified. The general intractability of the CSP and QCSP motivates the search for restricted cases of these problems that are polynomialtime tractable. In this
Some Pitfalls for Experimenters with Random SAT
 Artificial Intelligence
, 1996
"... We consider the use of random CNF formulas in evaluating the performance of SAT testing algorithms, and in particular the role that the phase transition phenomenon plays in this use. Examples from the literature illustrate the importance of understanding the properties of formula distributions prior ..."
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Cited by 19 (3 self)
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We consider the use of random CNF formulas in evaluating the performance of SAT testing algorithms, and in particular the role that the phase transition phenomenon plays in this use. Examples from the literature illustrate the importance of understanding the properties of formula distributions prior to designing an experiment. We expect this to be of increasing importance in the field. 1 Introduction Satisfiability testing lies at the core of many computational problems and because of its close relationship to various reasoning tasks, this is especially so in Artificial Intelligence. Randomly generated CNF formulas are a popular class of test problems for evaluating the performance of SAT testing programs. Not surprisingly, the choice of formula distribution is crucial to the validity of any investigation using random formulas. In [23], we argued that some families of distributions were more useful sources of test material than others, and suggested choosing formulas from the "hard reg...
On Stable Route Selection for Interdomain Traffic Engineering: Models and Analysis
, 2005
"... BGP route selection is increasingly being used by ASes to achieve interdomain traffic engineering objectives. One fundamental feature of route selection for interdomain traffic engineering is that routes for a set of destinations be chosen jointly to satisfy traffic engineering constraints and meet ..."
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Cited by 16 (4 self)
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BGP route selection is increasingly being used by ASes to achieve interdomain traffic engineering objectives. One fundamental feature of route selection for interdomain traffic engineering is that routes for a set of destinations be chosen jointly to satisfy traffic engineering constraints and meet traffic engineering objectives. In this paper, we present a general model of route selection for interdomain traffic engineering by allowing the routing of multiple destinations to be coordinated. We identify potential routing instability and inefficiency by showing that there exist networks where the interaction of the route selection of multiple destinations can cause routing instability, even though the networks are guaranteed to converge to a unique route selection when each destination is considered alone. We derive a sufficient condition to guarantee routing convergence. We also show that the constraints on local policies imposed by business considerations in the Internet can guarantee stability without global coordination. Using realistic Internet topology, we evaluate the extent to which routing instability of interdomain traffic engineering can happen when the constraints are violated. We further generalize
Study of lower bound functions for max2sat
 In AAAI2004
, 2004
"... Recently, several lower bound functions are proposed for solving the MAX2SAT problem optimally in a branchandbound algorithm. These lower bounds improve significantly the performance of these algorithms. Based on the study of these lower bound functions, we propose a new, lineartime lower bound ..."
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Cited by 11 (0 self)
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Recently, several lower bound functions are proposed for solving the MAX2SAT problem optimally in a branchandbound algorithm. These lower bounds improve significantly the performance of these algorithms. Based on the study of these lower bound functions, we propose a new, lineartime lower bound function. We show that the new lower bound function is admissible and it is consistently and substantially better than other known lower bound functions. The result of this study is a highperformance implementation of an exact algorithm for MAX2SAT which outperforms any implementation of the same class.