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128
GSAT and Dynamic Backtracking
 Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
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Cited by 390 (15 self)
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There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new technique that combines these two approaches. The algorithm allows substantial freedom of movement in the search space but enough information is retained to ensure the systematicity of the resulting analysis. Bounds are given for the size of the justification database and conditions are presented that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision, and examples include propositional theorem proving, map coloring and scheduling problems. The probl...
Boosting combinatorial search through randomization
, 1998
"... Unpredictability in the running time of complete search procedures can often be explained by the phenomenon of “heavytailed cost distributions”, meaning that at any time during the experiment there is a nonnegligible probability of hitting a problem that requires exponentially more time to solve t ..."
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Cited by 359 (34 self)
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Unpredictability in the running time of complete search procedures can often be explained by the phenomenon of “heavytailed cost distributions”, meaning that at any time during the experiment there is a nonnegligible probability of hitting a problem that requires exponentially more time to solve than any that has been encountered before (Gomes et al. 1998a). We present a general method for introducing controlled randomization into complete search algorithms. The “boosted ” search methods provably eliminate heavytails to the right of the median. Furthermore, they can take advantage of heavytails to the left of the median (that is, a nonnegligible chance of very short runs) to dramatically shorten the solution time. We demonstrate speedups of several orders of magnitude for stateoftheart complete search procedures running on hard, realworld problems.
Limited Discrepancy Search
 In Proceedings IJCAI’95
, 1995
"... Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Li ..."
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Cited by 307 (5 self)
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Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Limited discrepancy search addresses the problem of what to do when the heuristics fail. Our intuition is that a failing heuristic might well have succeeded if it were not for a small number of "wrong turns " along the way. For a binary tree of height d, there are only d ways the heuristic could make a single wrong turn, and only d(di)/2 ways it could make two. A small number of wrong turns can be overcome by systematically searching all paths that differ from the heuristic path in at most a small number of decision points, or "discrepancies." Limited discrepancy search is a backtracking algorithm that searches the nodes of the tree in increasing order of such discrepancies. We show formally and experimentally that limited discrepancy search can be expected to outperform existing approaches. 1
Using CSP lookback techniques to solve realworld SAT instances
, 1997
"... We report on the performance of an enhanced version of the “DavisPutnam ” (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback tec ..."
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Cited by 238 (1 self)
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We report on the performance of an enhanced version of the “DavisPutnam ” (DP) proof procedure for propositional satisfiability (SAT) on large instances derived from realworld problems in planning, scheduling, and circuit diagnosis and synthesis. Our results show that incorporating CSP lookback techniques especially the relatively new technique of relevancebounded learning renders easy many problems which otherwise are beyond DP’s reach. Frequently they make DP, a systematic algorithm, perform as well or better than stochastic SAT algorithms such as GSAT or WSAT. We recommend that such techniques be included as options in implementations of DP, just as they are in systematic algorithms for the more general constraint satisfaction problem.
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.
HeavyTailed Phenomena in Satisfiability and Constraint Satisfaction Problems
 J. of Autom. Reasoning
, 2000
"... Abstract. We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by ver ..."
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Cited by 164 (27 self)
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Abstract. We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or “heavy tails”. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavytailed behavior. Furthermore, for harder problem instances, we observe long tails on the lefthand side of the distribution, which is indicative of a nonnegligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavytailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis. Key words: satisfiability, constraint satisfaction, heavy tails, backtracking 1.
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 139 (22 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.
Bridging the gap between planning and scheduling
 KNOWLEDGE ENGINEERING REVIEW
, 2000
"... Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting orde ..."
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Cited by 115 (12 self)
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Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting ordering problem is hard. In this paper, we give an overview of AI planning and scheduling techniques, focusing on their similarities, differences, and limitations. We also argue that many difficult practical problems lie somewhere between planning and scheduling, and that neither area has the right set of tools for solving these vexing problems.
Depthbounded Discrepancy Search
 In Proceedings of IJCAI97
, 1997
"... Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of finding a goal in a limited amount of search. Depthbounded discrepancy search offers such a hope. The motivation behind depthbounde ..."
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Cited by 87 (0 self)
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Many search trees are impractically large to explore exhaustively. Recently, techniques like limited discrepancy search have been proposed for improving the chance of finding a goal in a limited amount of search. Depthbounded discrepancy search offers such a hope. The motivation behind depthbounded discrepancy search is that branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We therefore combine one of the best features of limited discrepancy search  the ability to undo early mistakes  with the completeness of iterative deepening search. We show theoretically and experimentally that this novel combination outperforms existing techniques. 1 Introduction On backtracking, depthfirst search explores decisions made against the branching heuristic (or "discrepancies "), starting with decisions made deep in the search tree. However, branching heuristics are more likely to be wrong at the top of the tree than at the bottom. We would like theref...
A General Stochastic Approach to Solving Problems with Hard and Soft Constraints
 The Satisfiability Problem: Theory and Applications
, 1996
"... . Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable  in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost functi ..."
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Cited by 62 (1 self)
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. Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable  in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost function) . Preferences can be encoded by incorporating "soft" constraints in the problem instance. We show how both hard and soft constraints can be handled by encoding problems as instances of weighted MAXSAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize a localsearch algorithm for satisfiability to handle weighted MAXSAT. To demonstrate the effectiveness of our approach, we present experimental results on encodings of a set of wellstudied network Steinertree problems. This approach turns out to be competitive with some of the best current specialized algorithms developed in operations research. 1. Introduction Traditi...