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27
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 176 (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.
Testing Heuristics: We Have It All Wrong
 Journal of Heuristics
, 1995
"... The competitive nature of most algorithmic experimentation is a source of problems that are all too familiar to the research community. It is hard to make fair comparisons between algorithms and to assemble realistic test problems. Competitive testing tells us which algorithm is faster but not w ..."
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Cited by 145 (3 self)
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The competitive nature of most algorithmic experimentation is a source of problems that are all too familiar to the research community. It is hard to make fair comparisons between algorithms and to assemble realistic test problems. Competitive testing tells us which algorithm is faster but not why. Because it requires polished code, it consumes time and energy that could be spent doing more experiments. This paper argues that a more scientific approach of controlled experimentation, similar to that used in other empirical sciences, avoids or alleviates these problems. We have confused research and development; competitive testing is suited only for the latter. Most experimental studies of heuristic algorithms resemble track meets more than scientific endeavors. Typically an investigator has a bright idea for a new algorithm and wants to show that it works better, in some sense, than known algorithms. This requires computational tests, perhaps on a standard set of benchmark p...
A DavisPutnam Based Enumeration Algorithm for Linear PseudoBoolean Optimization
, 1995
"... The DavisPutnam enumeration method (DP) has recently become one of the fastest known methods for solving the clausal satisfiability problem of propositional calculus. We present a generalization of the DPprocedure for solving the satisfiability problem of a set of linear pseudoBoolean (or 01) ..."
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Cited by 127 (2 self)
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The DavisPutnam enumeration method (DP) has recently become one of the fastest known methods for solving the clausal satisfiability problem of propositional calculus. We present a generalization of the DPprocedure for solving the satisfiability problem of a set of linear pseudoBoolean (or 01) inequalities. We extend the method to solve linear 01 optimization problems, i.e. optimize a linear pseudoBoolean objective function w.r.t. a set of linear pseudoBoolean inequalities. The algorithm compares well with traditional linear programming based methods on a variety of standard 01 integer programming benchmarks.
Needed: An Empirical Science Of Algorithms
 Operations Research
, 1994
"... this article goes to press. Journal editors can be encouraged to seek out referees who have done rigorous empirical studies. Refereeing standards will evolve, particularly as the empirical science develops. ..."
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Cited by 87 (4 self)
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this article goes to press. Journal editors can be encouraged to seek out referees who have done rigorous empirical studies. Refereeing standards will evolve, particularly as the empirical science develops.
Logicbased benders decomposition
, 2000
"... Benders decomposition uses a strategy of “learning from one’s mistakes.” The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an “inference dual. ” Solution of the inference dual take ..."
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Benders decomposition uses a strategy of “learning from one’s mistakes.” The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an “inference dual. ” Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different from other generalized duals that have been proposed. The approach is illustrated by working out the details for propositional satisfiability and 01 programming problems. Computational tests are carried out for the latter, but the most promising contribution of logicbased Benders may be to provide a framework for combining optimization and constraint programming methods.
Stochastic Boolean Satisfiability
 Journal of Automated Reasoning
, 2000
"... . Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stoc ..."
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Cited by 65 (9 self)
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. Satisfiability problems and probabilistic models are core topics of artificial intelligence and computer science. This paper looks at the rich intersection between these two areas, opening the door for the use of satisfiability approaches in probabilistic domains. The paper examines a generic stochastic satisfiability problem, SSat, which can function for probabilistic domains as Sat does for deterministic domains. It shows the connection between SSat and well studied problems in belief network inference and planning under uncertainty, and defines algorithms, both systematic and stochastic, for solving SSat instances. These algorithms are validated on random SSat formulae generated under the fixedclause model. In spite of the large complexity gap between SSat (PSPACE) and Sat (NP), the paper suggests that much of what we've learned about Sat transfers to the probabilistic domain. 1. Introduction There has been a recent focus in artificial intelligence (AI) on solving problems exh...
A Grasp For Satisfiability
 CLIQUES, COLORING, AND SATISFIABILITY: THE SECOND DIMACS IMPLEMENTATION CHALLENGE, VOLUME 26 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1996
"... A greedy randomized adaptive search procedure (Grasp) is a randomized heuristic that has been shown to quickly produce good quality solutions for a wide variety of combinatorial optimization problems. In this paper, we describe a Grasp for the satisfiability (SAT) problem. This algorithm can be also ..."
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Cited by 30 (6 self)
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A greedy randomized adaptive search procedure (Grasp) is a randomized heuristic that has been shown to quickly produce good quality solutions for a wide variety of combinatorial optimization problems. In this paper, we describe a Grasp for the satisfiability (SAT) problem. This algorithm can be also directly applied to both the weighted and unweighted versions of the maximum satisfiability (MAXSAT) problem. We review basic concepts of Grasp: construction and local search algorithms. The implementation of Grasp for the SAT problem is described in detail. Computational experience on a large set of test problems is presented.
Logic cuts for processing networks with fixed charges
 Comput. Oper. Res
, 1994
"... Logic cuts for processing networks with fixed charges ..."
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Cited by 24 (9 self)
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Logic cuts for processing networks with fixed charges
Partial Instantiation Methods for Inference in First Order Logic
 Journal of Automated Reasoning
, 2000
"... Satisfiability algorithms for propositional logic have improved enormously in recently years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. R. Jeroslow introduced a partial instantiati ..."
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Satisfiability algorithms for propositional logic have improved enormously in recently years. This increases the attractiveness of satisfiability methods for first order logic that reduce the problem to a series of groundlevel satisfiability problems. R. Jeroslow introduced a partial instantiation method of this kind that differs radically from the standard resolutionbased methods. This paper lays the theoretical groundwork for an extension of his method that is general enough and efficient enough for general logic programming with indefinite clauses. In particular we improve Jeroslow's approach by (a) extending it to logic with functions, (b) accelerating it through the use of satisfiers, as introduced by Gallo and Rago, and (c) simplifying it to obtain further speedup. We provide a similar development for a "dual" partial instantiation approach defined by Hooker and suggest a primal/dual strategy. We prove correctness of the primal and dual algorithms for full firstorder ...
Logical Inference and Polyhedral Projection
 Proceeedings, Computer Science Logic Workshop (CSL'91), Lecture Notes in Computer Science 626
, 1992
"... We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral pro ..."
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We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral projection partially solves this problem and in particular derives precisely those inferences that can be obtained by a certain form of unit resolution. We prove that this unit resolution algorithm is exponential in the number of atoms in the restricted set but is polynomial in the problem size when this number of fixed. We also survey a number of new satisfiability algorithms that have been suggested by the polyhedral interpretation of propositional logic. 1 Introduction The inference problem in propositional logic is closely connected with polyhedral theory. In the last few years this connection has suggested a number of new inference algorithms that have substantially advanced the st...