A filtering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation

Janssen, Pierre; Jégou, Philippe; Nouguier, B.; Vilarem, Marie-Catherine

doi:10.1109/tai.1989.65349

Cited by 41 publications

(55 citation statements)

References 11 publications

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“…Despite previous work showing that NIC may be too costly to use in general [5], our experimental results show that there are instances that benefit from higher level consistency. The algorithm we use to remove redundant edges from a dual graph generates triangle-shaped grids for binary CSPs [10]. However, there may also be non-grid shaped minimal dual graphs.…”

Section: Discussionmentioning

confidence: 99%

“…Neigh(R i ) denotes the set of relations adjacent to a relation R i in the dual graph. Janssen et al [10] and Dechter [6] observed that, in the dual graph, an edge between two vertices is redundant if there exists an alternate path between the two vertices such that the shared variables appear in every vertex in the path. Redundant edges can be removed without modifying the set of solutions.…”

Section: Graphical Representationsmentioning

confidence: 99%

“…Redundant edges can be removed without modifying the set of solutions. Janssen et al introduced an efficient algorithm for computing the minimal dual graph [10]. Many minimal graphs may exist, but all are guaranteed to have the same number of edges.…”

Section: Graphical Representationsmentioning

confidence: 99%

See 2 more Smart Citations

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Woodward

Karakashian

Choueiry

et al. 2012

Lecture Notes in Computer Science

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Abstract. Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems (CSPs). As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational Neighborhood Inverse Consistency (RNIC), which is a consistency property that we had introduced for non-binary CSPs [17]. We discuss how the structure of the dual graph of binary CSPs affects the consistency level enforced by RNIC. Then, we compare, both theoretically and empirically, RNIC to Neighborhood Inverse Consistency (NIC) and strong Conservative Dual Consistency (sCDC), which are higherlevel consistency properties useful for solving difficult problem instances. We show that all three properties are pairwise incomparable.

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Section: Discussionmentioning

confidence: 99%

Section: Graphical Representationsmentioning

confidence: 99%

See 1 more Smart Citation

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Woodward

Karakashian

Choueiry

et al. 2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…These approaches, however, have in common that consistency checks are done separately and independently for each constraint. Higher-order consistencies, such as pairwise consistency [12] can consider multiple constraints simultaneously, but may suffer from a relatively high computational cost.…”

Section: Introductionmentioning

confidence: 99%

Improved Constraint Propagation via Lagrangian Decomposition

Bergman

Ciré

Hoeve

2015

Lecture Notes in Computer Science

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Always cite the published version, so the author(s) will receive recognition through services that track citation counts, e.g. Scopus. If you need to cite the page number of the author manuscript from TSpace because you cannot access the published version, then cite the TSpace version in addition to the published version using the permanent URI (handle) found on the record page.This article was made openly accessible by U of T Faculty. Please tell us how this access benefits you. Your story matters. Improved Constraint Propagation viaLagrangian Decomposition Abstract. Constraint propagation is inherently restricted to the local information that is available to each propagator. We propose to improve the communication between constraints by introducing Lagrangian penalty costs between pairs of constraints, based on the Lagrangian decomposition scheme. The role of these penalties is to force variable assignments in each of the constraints to correspond to one another. We apply this approach to constraints that can be represented by decision diagrams, and show that propagating Lagrangian cost information can help improve the overall bound computation as well as the solution time.

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“…8,5,16 In contrast, little work had been done on such consistencies for non-binary constraints until very recently, whereas a number of consistencies that are stronger than GAC, but not domain filtering, have been developed. For example, pairwise consistency, 10 hyper-m-consistency, 12 relational consistency, 15 and ω-consistency. 13 However, these consistencies are rarely used in practice, mainly because they have a high space complexity.…”

Section: Introductionmentioning

confidence: 99%

Strong Domain Filtering Consistencies for Non-Binary Constraint Satisfaction Problems

Stergiou

2008

Int. J. Artif. Intell. Tools

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Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with non-binary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong domain filtering consistencies for non-binary constraints and theoretically compare their pruning power. We prove that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for domain filtering consistencies in non-binary CSPs. We show how this algorithm can be instantiated to enforce some of the proposed consistencies and analyze the worst-case complexities of the resulting algorithms. Finally, we make a preliminary empirical study.

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A filtering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation

Cited by 41 publications

References 11 publications

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Revisiting Neighborhood Inverse Consistency on Binary CSPs

Improved Constraint Propagation via Lagrangian Decomposition

Strong Domain Filtering Consistencies for Non-Binary Constraint Satisfaction Problems

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