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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 350 (7 self)
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problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflictdirected backjumping
Nogood Recording for Static and Dynamic Constraint Satisfaction Problems
 International Journal of Artificial Intelligence Tools
, 1993
"... Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, fo ..."
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Cited by 111 (5 self)
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Many AI synthesis problems such as planning, scheduling or design may be encoded in a constraint satisfaction problem (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks, the set of constraints to consider may evolve because of the environment or because of user interactions. The problem we consider here is the solution maintenance problem in such a dynamic CSP (DCSP). We propose a new class of constraint recording algorithms called Nogood Recording that may be used for solving both static and dynamic CSPs. It offers an interesting compromise, polynomially bounded in space, between an ATMSlike approach and the usual static constraint satisfaction algorithms. 1 Introduction The constraint satisfaction problem (CSP) model is widely used to represent and solve various AI related problems and provides fundamental tools in areas such as truth...
Domain Filtering Consistencies
 Journal of Artificial Intelligence Research (JAIR)
, 2001
"... Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been kn ..."
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Cited by 54 (5 self)
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Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.
A Tutorial on Constraint Programming
 University of Leeds
, 1995
"... A constraint satisfaction problem (CSP) consists of a set of variables; for each variable, a finite set of possible values (its domain); and a set of constraints restricting the values that the variables can simultaneously take. A solution to a CSP is an assignment of a value from its domain to ever ..."
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Cited by 30 (3 self)
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A constraint satisfaction problem (CSP) consists of a set of variables; for each variable, a finite set of possible values (its domain); and a set of constraints restricting the values that the variables can simultaneously take. A solution to a CSP is an assignment of a value from its domain to every variable, in such a way that every constraint is satisfied. Many problems arising in O.R., in particular scheduling, timetabling and other combinatorial problems, can be represented as CSPs. Constraint programming tools now exist which allow CSPs to be expressed easily, and provide standard strategies for finding solutions. This tutorial is intended to give a basic grounding in constraint satisfaction problems and some of the algorithms used to solve them, including the techniques commonly used in constraint programming tools. In particular, it covers arc and path consistency; simple backtracking and forward checking, as examples of search algorithms; and the use of heuristics to guide the...
ArcConsistency in Dynamic CSPs Is No More Prohibitive
 In 8 th Conference on Tools with Artificial Intelligence (TAI’96
, 1996
"... Constraint satisfaction problems (CSPs) are widely used in Artificial Intelligence. The problem of the existence of a solution in a CSP being NPcomplete, filtering techniques and particularly arcconsistency are essential. They remove some local inconsistencies and so make the search easier. Since ..."
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Cited by 19 (2 self)
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Constraint satisfaction problems (CSPs) are widely used in Artificial Intelligence. The problem of the existence of a solution in a CSP being NPcomplete, filtering techniques and particularly arcconsistency are essential. They remove some local inconsistencies and so make the search easier. Since many problems in AI require a dynamic environment, the model was extended to dynamic CSPs (DCSPs) and some incremental arcconsistency algorithms were proposed. However, all of them have important drawbacks. DnAC4 has an expensive worstcase space complexity and a bad average time complexity. ACjDC has a nonoptimal worstcase time complexity which prevents from taking advantage of its good space complexity. The algorithm we present in this paper has both lower space requirements and better time performances than DnAC4 while keeping an optimal worst case time complexity. 1. Introduction Constraint satisfaction problems (CSPs) occur widely in Artificial Intelligence. They have shown their ...
Maintaining Arc Consistency through Constraint Retraction
 Proc. TAI94, IEEE
, 1994
"... To cope with a growing number of applications, the basic formalism of constraint satisfaction problems has to be augmented in various directions. One of these directions is the concept of dynamic constraint problems i.e. problems to which constraints can be added but also retracted at any time. To h ..."
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Cited by 15 (0 self)
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To cope with a growing number of applications, the basic formalism of constraint satisfaction problems has to be augmented in various directions. One of these directions is the concept of dynamic constraint problems i.e. problems to which constraints can be added but also retracted at any time. To handle dynamic problems, it is important to adapt efficiently the solving procedures that are available on static ones. Of particular interest is the arcconsistency enforcement procedure; the goal of the paper is to present an adaptation of it to dynamic problems. Contrary to previous approaches, the one presented here does not rely on any reason maintenance system and consequently has the advantage of a low space complexity. The detailed algorithm of the procedure is given and an experimental evaluation of its performances is displayed. Some benefits gained by the approach regarding flexibility and extensibility are highlighted. 1 Introduction Arcconsistency (ac) procedures are essential ...
ArcConsistency for Dynamic Constraint Problems: An RMSFree Approach
 In Proceedings ECAI’94 Workshop on Constraint Satisfaction Issues raised by Practical Applications
, 1994
"... With the rapid development of constraint programminghas emerged the need for consistency maintenance procedures that support efficiently dynamic problems i.e. problems to which constraints can be added but also retracted. This paper presents such a procedure which, contrary to previous approaches, d ..."
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Cited by 6 (0 self)
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With the rapid development of constraint programminghas emerged the need for consistency maintenance procedures that support efficiently dynamic problems i.e. problems to which constraints can be added but also retracted. This paper presents such a procedure which, contrary to previous approaches, does not rely on any reason maintenance system and consequently has the advantage of a low space complexity. We give the detailed algorithm of the procedure and an experimental evaluation of its performances. We also highlight some benefits gained by our approach regarding flexibility and extensibility. 1 Introduction Arcconsistency (ac) procedures are essential preprocessing tools for the resolution of constraint satisfaction problems (csps). Their use is well suited to constraint problems that grow monotonically: keeping the arcconsistent state of a problem while adding constraints is simply a matter of restarting ac from the added constraints. ac procedures are thus inherently incremen...