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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 399 (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.
From Local to Global Consistency
, 1992
"... In reasoning tasks involving the maintenance of consistent databases (socalled QQconstraint networks/Q/Q), it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data. In this paper we present a relationship betwe ..."
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Cited by 115 (7 self)
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In reasoning tasks involving the maintenance of consistent databases (socalled QQconstraint networks/Q/Q), it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data. In this paper we present a relationship between the sizes of the variables' domains, the constraints' arity and the level of local consistency sufficient to ensure global consistency. Based on these parameters a new tractability classification of constraint networks is presented. We also show, based on this relationship, that any relation on bivalued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables.
Local and global relational consistency
 THEORETICAL COMPUTER SCIENCE
, 1997
"... Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consiste ..."
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Cited by 65 (13 self)
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Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consistency, which we characterize as variablebased. We show the conceptual power of the new definition by showing how it unifies known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for solving linear inequalities. Algorithms for enforcing various levels of relational consistency are introduced and analyzed. We also show the usefulness of the new definition in characterizing relationships between properties of constraint networks and the level of local consistency needed to ensure global consistency.
Characterising Tractable Constraints
 Artificial Intelligence
, 1994
"... Finding solutions to a binary constraint satisfaction problem is known to be an NPcomplete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. This paper considers restricted sets of contraints which are closed under pe ..."
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Cited by 58 (18 self)
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Finding solutions to a binary constraint satisfaction problem is known to be an NPcomplete problem in general, but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted. This paper considers restricted sets of contraints which are closed under permutation of the labels. We identify a set of constraints which gives rise to a class of tractable problems and give polynomial time algorithms for solving such problems, and for finding the equivalent minimal network. We also prove that the class of problems generated by any set of constraints not contained in this restricted set is NPcomplete. 1 Introduction Finding solutions to a constraint satisfaction problem is known to be an NPcomplete problem in general [11] even when the constraints are restricted to binary constraints. However, many of the problems which arise in practice have special properties which allow them to be solved efficiently. The question of identifying restrictions t...
Consistency Techniques for Continuous Constraints
 Constraints
, 1996
"... We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constrai ..."
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Cited by 58 (7 self)
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We consider constraint satisfaction problemswith variables in continuous,numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.
Constraint propagation
 Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 56 (4 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
Constraints, Consistency, and Closure
 Artificial Intelligence
, 1998
"... Although the constraint satisfaction problem is NPcomplete in general, a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency. In this paper, we describe a simple algebraic property which characterises all possi ..."
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Cited by 56 (12 self)
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Although the constraint satisfaction problem is NPcomplete in general, a number of constraint classes have been identified for which some fixed level of local consistency is sufficient to ensure global consistency. In this paper, we describe a simple algebraic property which characterises all possible constraint types for which strong kconsistency is sufficient to ensure global consistency, for each k ? 2. We give a number of examples to illustrate the application of this result. 1 Introduction The constraint satisfaction problem provides a framework in which it is possible to express, in a natural way, many combinatorial problems encountered in artificial intelligence and elsewhere. The aim in a constraint satisfaction problem is to find an assignment of values to a given set of variables subject to constraints on the values which can be assigned simultaneously to certain specified subsets of variables. The constraint satisfaction problem is known to be an NPcomplete problem in ge...
Tractable Disjunctions of Linear Constraints: Basic Results and Applications to Temporal Reasoning
 Theoretical Computer Science
, 1996
"... We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez an ..."
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Cited by 52 (3 self)
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We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fourier's algorithm for linear inequalities. Finally, we use these results to provide new temporal reasoning algorithms for the OrdHorn subclass of Allen's interval formalism. We also show that there is no low level of local consistency that can guarantee global consistency for the OrdHorn subclass. This property distinguishes the OrdHorn subclass from the pointizable subclass (for which strong 5consistency is sufficient to guarantee global consistency), and the continuous endpoint subclass (for whi...
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 ..."
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Cited by 52 (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...
Ordering Heuristics for Arc Consistency Algorithms
 In AI/GI/VI ’92
, 1992
"... Arc consistency algorithms are used in solving constraint satisfaction problems and are important in constraint logic programming languages. Search order heuristics for arc consistency algorithms significantly enhance the efficiency of their implementation. In this paper we propose and evaluate seve ..."
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Cited by 49 (3 self)
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Arc consistency algorithms are used in solving constraint satisfaction problems and are important in constraint logic programming languages. Search order heuristics for arc consistency algorithms significantly enhance the efficiency of their implementation. In this paper we propose and evaluate several ordering heuristics. Care is taken with experimental design, involving random problems, and statistical evaluation of results. A heuristic is identified which yields about 50% savings on average, using the standard measure of consistency pair checks, with reasonable heuristic computation cost. 1 Introduction Arc consistency insures that any two mutually constraining problem variables are mutually consistent: given a value for one, we can find a value for the other which satisfies the constraint between them. The constraint specifies which pairs of values can be simultaneously assumed by the pair of variables. Arc consistency is a fundamental concept in constraintbased reasoning [ Mack...