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44
Partial Constraint Satisfaction
, 1992
"... . A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying ..."
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Cited by 422 (23 self)
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. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...
GRASP: A Search Algorithm for Propositional Satisfiability
 IEEE Transactions on Computers
, 1999
"... AbstractÐThis paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several searchpruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techni ..."
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Cited by 370 (35 self)
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AbstractÐThis paper introduces GRASP (Generic seaRch Algorithm for the Satisfiability Problem), a new search algorithm for Propositional Satisfiability (SAT). GRASP incorporates several searchpruning techniques that proved to be quite powerful on a wide variety of SAT problems. Some of these techniques are specific to SAT, whereas others are similar in spirit to approaches in other fields of Artificial Intelligence. GRASP is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack nonchronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by ªrecordingº the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straightforward bookkeeping of the causality chains leading up to conflicts allows GRASP to identify assignments that are necessary for a solution to be found. Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for a large number of representative classes of SAT instances. Index TermsÐSatisfiability, search algorithms, conflict diagnosis, conflictdirected nonchronological backtracking, conflictbased equivalence, failuredriven assertions, unique implication points. 1
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 368 (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.
SemiringBased Constraint Satisfaction and Optimization
 JOURNAL OF THE ACM
, 1997
"... We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be asso ..."
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Cited by 159 (20 self)
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We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (1 and 3) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.
Backtracking Algorithms for Disjunctions of Temporal Constraints
 Artificial Intelligence
, 1998
"... We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. W ..."
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Cited by 106 (2 self)
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We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints. We have partially ordered those algorithms according to the number of visited search nodes and the number of performed consistency checks. Finally, we have carried out a series of experimental results on the location of the hard region. The results show that hard problems occur at a critical value of the ratio of disjunctions to variables. This value is between 6 and 7. Introduction Reasoning with temporal constraints has been a hot research topic for the last fifteen years. The importance of this problem has been demonstrated in many areas of artifici...
Directional Resolution: The DavisPutnam Procedure, Revisited
 IN PROCEEDINGS OF KR94
, 1994
"... The paper presents an algorithm called directional resolution, a variation on the original DavisPutnam algorithm, and analyzes its worstcase behavior as a function of the topological structure of propositional theories. The concepts of induced width and diversity are shown to play a key role in ..."
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Cited by 100 (21 self)
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The paper presents an algorithm called directional resolution, a variation on the original DavisPutnam algorithm, and analyzes its worstcase behavior as a function of the topological structure of propositional theories. The concepts of induced width and diversity are shown to play a key role in bounding the complexity of the procedure. The importance of our analysis lies in highlighting structurebased tractable classes of satisfiability and in providing theoretical guarantees on the time and space complexity of the algorithm. Contrary to previous assessments, we show that for many theories directional resolution could be an effective procedure. Our empirical tests confirm theoretical prediction, showing that on problems with a special structure, namely ktree embeddings (e.g. chains, (k,m)trees), directional resolution greatly outperforms one of the most effective satisfiability algorithms known to date, the popular DavisPutnam procedure. Furthermore, combining a bounded...
On the Equivalence of Constraint Satisfaction Problems
 In Proceedings of the 9th European Conference on Artificial Intelligence
, 1990
"... A solution of a Constraint Satisfaction Problem (CSP) is an assignment of values to all its variables such that all its constraints are satisfied. Usually two CSPs are considered equivalent if they have the same solution set. We find this definition limiting, and develop a more general definition ba ..."
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Cited by 84 (0 self)
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A solution of a Constraint Satisfaction Problem (CSP) is an assignment of values to all its variables such that all its constraints are satisfied. Usually two CSPs are considered equivalent if they have the same solution set. We find this definition limiting, and develop a more general definition based on the concept of mutual reducibility. In this extended scheme it is reasonable to consider a pair of CSPs equivalent even if they have different solutions. The basic idea behind the extended scheme is that two CSPs can be considered equivalent whenever they contain the same "amount of information", i.e. whenever it is possible to obtain the solution of one of them from the solution of the other one, and viceversa. In this way, both constraint and variable redundancy are allowed in CSPs belonging to the same equivalence class. As an example of the usefulness of this new notion of equivalence, we formally prove that binary and nonbinary CSPs are equivalent (in the new sense). Such a pro...
Structure Identification in Relational Data
, 1997
"... This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is give ..."
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Cited by 74 (2 self)
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This paper presents several investigations into the prospects for identifying meaningful structures in empirical data, namely, structures permitting effective organization of the data to meet requirements of future queries. We propose a general framework whereby the notion of identifiability is given a precise formal definition similar to that of learnability. Using this framework, we then explore if a tractable procedure exists for deciding whether a given relation is decomposable into a constraint network or a CNF theory with desirable topology and, if the answer is positive, identifying the desired decomposition. Finally, we
Lookahead value ordering for constraint satisfaction problems
 In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence
, 1995
"... Looking ahead during search is often useful when solving constraint satisfaction problems. Previous studies have shown that looking ahead helps by causing deadends to occur earlier in the search, and by providing information that is useful for dynamic variable ordering. In this paper, we show that ..."
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Cited by 70 (4 self)
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Looking ahead during search is often useful when solving constraint satisfaction problems. Previous studies have shown that looking ahead helps by causing deadends to occur earlier in the search, and by providing information that is useful for dynamic variable ordering. In this paper, we show that another benefit of looking ahead is a useful domain value ordering heuristic, which we call lookahead value ordering or LVO. LVO counts the number of times each value of the current variable conflicts with some value of a future variable, and the value with the lowest number of conflicts is chosen first. Our experiments show that lookahead value ordering can be of substantial benefit, especially on hard constraint satisfaction problems. 1
Experimental evaluation of preprocessing techniques in constraint satisfaction problems
 In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence
, 1989
"... This paper presents an evaluation of two orthogonal schemes for improving the efficiency of solving constraint satisfaction problems (CSPs). The first scheme involves a class of preprocessing techniques designed to make the representation of the CSP more explicit, including directionalarcconsisten ..."
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Cited by 53 (10 self)
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This paper presents an evaluation of two orthogonal schemes for improving the efficiency of solving constraint satisfaction problems (CSPs). The first scheme involves a class of preprocessing techniques designed to make the representation of the CSP more explicit, including directionalarcconsistency, directionalpathconsistency and adaptiveconsistency. The second scheme aims at improving the order in which variables are chosen for evaluation during the search. In the first part of the experiment we tested the performance of backtracking (and its common enhancementbackjumping) with and without each of the preprocessings techniques above. The results show that directional arcconsistency, a scheme which embodies the simplest form of constraint recording, outperforms all other preprocessing techniques. The results of the second part of the experiment suggest that the best variable ordering is achieved by the fixed maxcardinality search order. 1.