Extending the Broken Triangle Property tractable class of binary CSPs

Naanaa, Wady

doi:10.1145/2903220.2903230

Cited by 5 publications

(11 citation statements)

References 12 publications

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“…In this section, we show that it is possible to merge certain pairs of values even in the presence of some broken triangles. This idea was inspired by recent work by Naanaa [19] on a new extension of BTP. We call our new property m-wBTP: the parameter m defines the number of variables supporting the weakly broken triangles.…”

Section: Weakly Broken Trianglesmentioning

confidence: 99%

“…Naanaa has given two other generalisations of BTP which define tractable classes [18,19]. It has been shown [8] that the notion of directional rank k −1 [18] strictly generalises k-BTP.…”

Section: Definition 7 (K-btp [8])mentioning

confidence: 99%

“…The notion WBTP [19] inspired our definition of 1-wBTP, but is different. We first give the definition of WBTP before showing that it can be seen as a strictly stronger condition than 1-wBTP (and thus leads to less mergings).…”

Section: Definition 7 (K-btp [8])mentioning

confidence: 99%

“…This class has some interesting characteristics, both from a theoretical and practical viewpoint: it generalises existing language-based and structural classes and is solved in polynomial time by the algorithm MAC which is omnipresent in constraint solvers [20]. Besides, many extensions of the broken-triangle property have led to the definition of new tractable classes [8,10,11,14,18,19]. Local versions of the BTP have also given rise to novel reduction operations for CSP instances.…”

Section: Introductionmentioning

confidence: 99%

“…6 we show that it does allow us to define a tractable class. We also compare m-wBTP with certain other generalisations of BTP, such as k-BTP [8] and WBTP [19]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Extending Broken Triangles and Enhanced Value-Merging

Cooper

Mouelhi

Terrioux

2016

Lecture Notes in Computer Science

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 17155The contribution was presented at CP 2016 :http://cp2016.a4cp.org/ Abstract. Broken triangles constitute an important concept not only for solving constraint satisfaction problems in polynomial time, but also for variable elimination or domain reduction by merging domain values. Specifically, for a given variable in a binary arc-consistent CSP, if no broken triangle occurs on any pair of values, then this variable can be eliminated while preserving satisfiability. More recently, it has been shown that even when this rule cannot be applied, it could be possible that for a given pair of values no broken triangle occurs. In this case, we can apply a domain-reduction operation which consists in merging these values while preserving satisfiability.In this paper we show that under certain conditions, and even if there are some broken triangles on a pair of values, these values can be merged without changing the satisfiability of the instance. This allows us to define a stronger merging operation and a new tractable class of binary CSP instances. We report experimental trials on benchmark instances.

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Section: Weakly Broken Trianglesmentioning

confidence: 99%

“…Naanaa has given two other generalisations of BTP which define tractable classes [18,19]. It has been shown [8] that the notion of directional rank k −1 [18] strictly generalises k-BTP.…”

Section: Definition 7 (K-btp [8])mentioning

confidence: 99%

Section: Definition 7 (K-btp [8])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…6 we show that it does allow us to define a tractable class. We also compare m-wBTP with certain other generalisations of BTP, such as k-BTP [8] and WBTP [19]. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Extending Broken Triangles and Enhanced Value-Merging

Cooper

Mouelhi

Terrioux

2016

Lecture Notes in Computer Science

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Galois Connections for Patterns: An Algebra of Labelled Graphs

Cohen

Cooper

Jeavons

et al. 2021

Lecture Notes in Computer Science

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A pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

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Constraint Decomposition Based on Tractable Properties

Mouelhi

2016

2016 IEEE 28th International Conference on Tools With Artificial Intelligence (ICTAI)

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Extending the Broken Triangle Property tractable class of binary CSPs

Cited by 5 publications

References 12 publications

Extending Broken Triangles and Enhanced Value-Merging

Extending Broken Triangles and Enhanced Value-Merging

Galois Connections for Patterns: An Algebra of Labelled Graphs

Constraint Decomposition Based on Tractable Properties

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