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Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 127 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Truth Maintenance
, 1990
"... General purpose truth maintenance systems have received considerable attention in the past few years. This paper discusses the functionality of truth maintenance systems and compares various existing algorithms. Applications and directions for future research are also discussed. Introduction In 197 ..."
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Cited by 110 (3 self)
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General purpose truth maintenance systems have received considerable attention in the past few years. This paper discusses the functionality of truth maintenance systems and compares various existing algorithms. Applications and directions for future research are also discussed. Introduction In 1978 Jon Doyle wrote a masters thesis at the MIT AI Laboratory entitled "Truth Maintenance Systems for Problem Solving" [ Doyle, 1979 ] . In this thesis Doyle described an independent module called a truth maintenance system, or TMS, which maintained beliefs for general problem solving systems. In the twelve years since the appearance of Doyle's TMS a large body of literature has accumulated on truth maintenance. The seminal idea appears not to have been any particular technical mechanism but rather the general concept of an independent module for truth (or belief) maintenance. All truth maintenance systems manipulate proposition symbols and relationships between proposition symbols. I will use...
SATzilla: Portfoliobased Algorithm Selection for SAT
"... It has been widely observed that there is no single “dominant ” SAT solver; instead, different solvers perform best on different instances. Rather than following the traditional approach of choosing the best solver for a given class of instances, we advocate making this decision online on a perinst ..."
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Cited by 91 (16 self)
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It has been widely observed that there is no single “dominant ” SAT solver; instead, different solvers perform best on different instances. Rather than following the traditional approach of choosing the best solver for a given class of instances, we advocate making this decision online on a perinstance basis. Building on previous work, we describe SATzilla, an automated approach for constructing perinstance algorithm portfolios for SAT that use socalled empirical hardness models to choose among their constituent solvers. This approach takes as input a distribution of problem instances and a set of component solvers, and constructs a portfolio optimizing a given objective function (such as mean runtime, percent of instances solved, or score in a competition). The excellent performance of our SATzilla portfolios has been independently verified in the 2007 SAT Competition, where our SATzilla07 solvers won three gold, one silver and one bronze medal. In this article, we go well beyond SATzilla07 by making the portfolio construction scalable and completely automated, and improving it by integrating local search solvers as candidate solvers, by predicting performance score instead of runtime, and by using hierarchical hardness models that take into account different types of SAT instances. We demonstrate the effectiveness of these new techniques in extensive experimental results on data sets including instances from the most recent SAT competition. 1.
HeuristicBiased Stochastic Sampling
 In Proceedings of the Thirteenth National Conference on Artificial Intelligence
, 1996
"... This paper presents a search technique for scheduling problems, called HeuristicBiased Stochastic Sampling (HBSS). The underlying assumption behind the HBSS approach is that strictly adhering to a search heuristic often does not yield the best solution and, therefore, exploration off the heuristic ..."
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Cited by 78 (0 self)
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This paper presents a search technique for scheduling problems, called HeuristicBiased Stochastic Sampling (HBSS). The underlying assumption behind the HBSS approach is that strictly adhering to a search heuristic often does not yield the best solution and, therefore, exploration off the heuristic path can prove fruitful. Within the HBSS approach, the balance between heuristic adherence and exploration can be controlled according to the confidence one has in the heuristic. By varying this balance, encoded as a bias function, the HBSS approach encompasses a family of search algorithms of which greedy search and completely random search are extreme members. We present empirical results from an application of HBSS to the realworld problem of observation scheduling. These results show that with the proper bias function, it can be easy to outperform greedy search. Introducing HBSS This paper presents a search technique, called HeuristicBiased Stochastic Sampling (HBSS), that was design...
A rearrangement search strategy for determining propositional satisfiability
 in Proceedings of the National Conference on Artificial Intelligence
, 1988
"... We present a simple algorithm for determining the satis ability of propositional formulas in Conjunctive Normal Form. As the procedure searches for a satisfying truth assignment it dynamically rearranges the order in which variables are considered. The choice of which variable to assign a truth valu ..."
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Cited by 74 (1 self)
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We present a simple algorithm for determining the satis ability of propositional formulas in Conjunctive Normal Form. As the procedure searches for a satisfying truth assignment it dynamically rearranges the order in which variables are considered. The choice of which variable to assign a truth value next is guided by an upper bound on the size of the search remaining � the procedure makes the choice which yields the smallest upper bound on the size of the remaining search. We describe several upper bound functions and discuss the tradeo between accurate upper bound functions and the overhead required to compute the upper bounds. Experimental data shows that for one easily computed upper bound the reduction in the size of the search space more than compensates for the overhead involved in selecting the next variable. 1
Solving Large Quadratic Assignment Problems on Computational Grids
, 2000
"... The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computat ..."
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Cited by 68 (6 self)
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The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a stateoftheart branchandbound algorithm running on a federation of geographically distributed resources known as a computational grid. Solution of QAPs of unprecedented complexity, including the nug30, kra30b, and tho30 instances, is reported.
Nonsystematic Backtracking Search
, 1995
"... Many practical problems in Artificial Intelligence have search trees that are too large to search exhaustively in the amount of time allowed. Systematic techniques such as chronological backtracking can be applied to these problems, but the order in which they examine nodes makes them unlikely to fi ..."
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Cited by 55 (1 self)
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Many practical problems in Artificial Intelligence have search trees that are too large to search exhaustively in the amount of time allowed. Systematic techniques such as chronological backtracking can be applied to these problems, but the order in which they examine nodes makes them unlikely to find a solution in the explored fraction of the space. Nonsystematic techniques have been proposed to alleviate the problem by searching nodes in a random order. A technique known as iterative sampling follows random paths from the root of the tree to the fringe, stopping if a path ends at a goal node. Although the nonsystematic techniques do not suffer from the problem of exploring nodes in a bad order, they do reconsider nodes they have already ruled out, a problem that is serious when the density of solutions in the tree is low. Unfortunately, for many practical problems the order of examing nodes matters and the density of solutions is low. Consequently, neither chronological backtracking...
A general backtrack algorithm that eliminates most redundant tests
, 1977
"... We define a faster algorithm functionally equivalent to the classical backtrack algorithm for assignment problems, of which the Eight Queens puzzle is an elementary example (Fillmore & Williamson 1974, Knuth 1975]. Experimental measurements (figure 1) reveal reduction by a factor of 2.5 for the 8qu ..."
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Cited by 53 (0 self)
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We define a faster algorithm functionally equivalent to the classical backtrack algorithm for assignment problems, of which the Eight Queens puzzle is an elementary example (Fillmore & Williamson 1974, Knuth 1975]. Experimental measurements (figure 1) reveal reduction by a factor of 2.5 for the 8queens puzzle (factor of 8.7 for 16 queens) in T, the number of pairtests performed before finding a solution (i.e., first solution). A pairtest in this case determines whether a queen on square (ij, jj) attacks a queen on square (12, j2 ^ i n C P U " seconds, net speedup is by a factor of 2.0 and 6.0 for 8and 16queens, respectively. 16queens was solved in 0.14 seconds on a PDP KL/10. The speedup can be attributed to the elimination of almost all redundant tests otherwise recomputed in many parts of the search tree, as indicated
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...