On a new extension of BTP for binary CSPs

Mouelhi, Achref El

doi:10.1007/s10601-018-9290-9

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…Hence, several relaxations of the BTP free property have been studied. In particular, m-fBTP (El Mouelhi, 2017, 2018 implies tractability using arc-consistency or arc-consistency with forward checking.…”

Section: Related Researchmentioning

confidence: 99%

Testing Unsatisfiability of Constraint Satisfaction Problems via Tensor Products

Gaur¹,

Khan²

2020

Preprint

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We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to decompose the microstructure into graph tensors. We show how to use the tensor decomposition to compute a proof of unsatisfiability efficiently and in parallel. We also offer substantial empirical evidence that our approach improves the praxis. For instance, one decomposition yields proofs of unsatisfiability in half the time without sacrificing the quality. Another decomposition is twenty times faster and effective three-tenths of the times compared to the prior method. Our method is applicable to arbitrary CSPs using the well known dual and hidden variable transformations from an arbitrary CSP to a binary CSP.

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Section: Related Researchmentioning

confidence: 99%

Testing Unsatisfiability of Constraint Satisfaction Problems via Tensor Products

Gaur¹,

Khan²

2020

Preprint

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“…The presence of some broken triangles on a given variable does not preclude value-merging or variable-elimination (while leaving satisfiability invariant): new solutions will not be introduced if the broken triangles lack support on some set of other variables (Cooper, El Mouelhi, & Terrioux, 2016b;El Mouelhi, 2018;Naanaa, 2016). Unfortunately, the search for lack-of-support variables for each broken triangle may render such techniques prohibitively expensive in terms of time complexity (since, in the worst case, the number of broken triangles is Θ(n 3 d 4 )).…”

Section: From Broken Triangles To Broken Polyhedramentioning

confidence: 99%

Variable Elimination in Binary CSPs

Cooper

Mouelhi

Terrioux

2019

jair

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We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with counting and quantification over variables and values. We propose new rules and compare them, both theoretically and experimentally. We give optimised algorithms to apply these rules and show that each define a novel tractable class. Using our variable-elimination rules in preprocessing allowed us to solve more benchmark problems than without.

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On a new extension of BTP for binary CSPs

Cited by 2 publications

References 22 publications

Testing Unsatisfiability of Constraint Satisfaction Problems via Tensor Products

Testing Unsatisfiability of Constraint Satisfaction Problems via Tensor Products

Variable Elimination in Binary CSPs

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