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94
Minimizing Conflicts: A Heuristic Repair Method for ConstraintSatisfaction and Scheduling Problems
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 1993
"... This paper describes a simple heuristic approach to solving largescale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a valueorder ..."
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Cited by 399 (6 self)
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This paper describes a simple heuristic approach to solving largescale constraint satisfaction and scheduling problems. In this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs. The search can be guided by a valueordering heuristic, the minconflicts heuristic, that attempts to minimize the number of constraint violations after each step. The heuristic can be used with a variety of different search strategies. We demonstrate empirically that on the nqueens problem, a technique based on this approach performs orders of magnitude better than traditional backtracking techniques. We also describe a scheduling application where the approach has been used successfully. A theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective.
Algorithms for Constraint Satisfaction Problems: A Survey
 AI MAGAZINE
, 1992
"... A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic ..."
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Cited by 371 (0 self)
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A large variety of problems in Artificial Intelligence and other areas of computer science can be viewed as a special case of the constraint satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, planning genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This paper presents a brief overview of many of these approaches in a tutorial fashion.
Hybrid Algorithms for the Constraint Satisfaction Problem
 Computational Intelligence
, 1993
"... problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflictdirected backjumping ..."
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Cited by 347 (7 self)
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problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflictdirected backjumping
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 160 (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.
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 124 (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...
A Theoretical Evaluation of Selected Backtracking Algorithms
 Artificial Intelligence
, 1997
"... In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on charact ..."
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Cited by 112 (2 self)
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In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a di erent, purely theoretical approach, which is based on characterizations of the sets of search treenodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such wellknown concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove the correctness of Backjumping and Con ictDirected Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modi cation to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Con ictDirected Backjumping (BMCBJ), so that they always perform fewer consistency checks than the original algorithms. 1
Automatically configuring constraint satisfaction programs: A case study
 CONSTRAINTS
, 1996
"... Multitac is a learning system that synthesizes heuristic constraint satisfaction programs. The system takes a library of generic algorithms and heuristics and specializes them for a particular application. We present a detailed case study with three different distributions ofa single combinatorial ..."
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Cited by 91 (4 self)
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Multitac is a learning system that synthesizes heuristic constraint satisfaction programs. The system takes a library of generic algorithms and heuristics and specializes them for a particular application. We present a detailed case study with three different distributions ofa single combinatorial problem, "Minimum Maximal Matching", and show that Multitac can synthesize programs for these different distributions that perform on par with handcoded programs and that exceed the performance of some wellknown satisfiability algorithms. In synthesizing a program, Multitac bases its choice of heuristics on an instance distribution, and we demonstrate that this capability has a significant impact on the results.
Distributed constrained heuristic search
 IEEE Transactions on Systems, Man, and Cybernetics
, 1991
"... In this paper we present a model of decentralized problem solving, called Distributed Constrained Heuristic Search (DCHS) that provides both structure and focus in individual agent search spaces so as to optimize decisions in the global space. The model achieves this by integrating decentralized con ..."
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Cited by 90 (11 self)
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In this paper we present a model of decentralized problem solving, called Distributed Constrained Heuristic Search (DCHS) that provides both structure and focus in individual agent search spaces so as to optimize decisions in the global space. The model achieves this by integrating decentralized constraint satisfaction and heuristic search. It is a formalism suitable for describing a large set of DAI problems. We introduce the notion of textures that allow agents to operate in an asynchronous concurrent manner. The employment of textures coupled with distributed asynchronous backjumping (DAB), a type of distributed dependencydirected backtracking that we have developed, enables agents to instantiate variables in such a way as to substantially reduce backtracking. We have experimentally tested our approach in the domain of decentralized jobshop scheduling. A formulation of distributed jobshop scheduling as a DCHS is presented as well as experimental results.
Probabilistic Verification of Discrete Event Systems using Acceptance Sampling
 In Proc. 14th International Conference on Computer Aided Verification, volume 2404 of LNCS
, 2002
"... We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in ..."
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Cited by 75 (10 self)
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We propose a model independent procedure for verifying properties of discrete event systems. The dynamics of such systems can be very complex, making them hard to analyze, so we resort to methods based on Monte Carlo simulation and statistical hypothesis testing. The verification is probabilistic in two senses. First, the properties, expressed as CSL formulas, can be probabilistic. Second, the result of the verification is probabilistic, and the probability of error is bounded by two parameters passed to the verification procedure. The verification of properties can be carried out in an anytime manner by starting off with loose error bounds, and gradually tightening these bounds.
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