Mapping Problems with Finite-Domain Variables to Problems with Boolean Variables

Ansótegui, Carlos; Manyà, Felip

doi:10.1007/11527695_1

Cited by 60 publications

(52 citation statements)

References 14 publications

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“…A large body of research exists on encoding constraints into CNF [16,23,22,11,13,12,6,1,10,4]. In addition, dedicated encodings have been proposed for specific types of constraints, including cardinality constraints [2,3].…”

Section: Related Workmentioning

confidence: 99%

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Towards Robust CNF Encodings of Cardinality Constraints

Marques-Silva

Lynce

Principles and Practice of Constraint Programming – CP 2007

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Abstract. Motivated by the performance improvements made to SAT solvers in recent years, a number of different encodings of constraints into SAT have been proposed. Concrete examples are the different SAT encodings for ≤ 1 (x1, . . . , xn) constraints. The most widely used encoding is known as the pairwise encoding, which is quadratic in the number of variables in the constraint. Alternative encodings are in general linear, and require using additional auxiliary variables. In most settings, the pairwise encoding performs acceptably well, but can require unacceptably large Boolean formulas. In contrast, linear encodings yield much smaller Boolean formulas, but in practice SAT solvers often perform unpredictably. This lack of predictability is mostly due to the large number of auxiliary variables that need to be added to the resulting Boolean formula. This paper studies one specific encoding for ≤ 1 (x1, . . . , xn) constraints, and shows how a state-of-the-art SAT solver can be adapted to overcome the problem of adding additional auxiliary variables. Moreover, the paper shows that a SAT solver may essentially ignore the existence of auxiliary variables. Experimental results indicate that the modified SAT solver becomes significantly more robust on SAT encodings involving ≤ 1 (x1, . . . , xn) constraints.

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Section: Related Workmentioning

confidence: 99%

“…. , x n ) constraints [11,13,1]. Observe that, given the straightforward CNF encoding of ≥ 1 (x 1 , .…”

Section: Introductionmentioning

confidence: 99%

Towards Robust CNF Encodings of Cardinality Constraints

Marques-Silva

Lynce

Principles and Practice of Constraint Programming – CP 2007

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“…The authors of the order encoding took a different approach [23], also used in [3,11]. In this encoding each Boolean variable represents a comparison, v ≤ c.…”

Section: The Order Encodingmentioning

confidence: 99%

“…A full regular encoding [3] introduces a Boolean variable x ≥ v,a for each inequality of the form v ≥ a. It can be based on any sparse encoding.…”

Section: Full Regular Encodingsmentioning

confidence: 99%

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The Order Encoding: From Tractable CSP to Tractable SAT

Petke

Jeavons

2011

Theory and Applications of Satisfiability Testing - SAT 2011

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Many mathematical and practical problems can be expressed as constraint satisfaction problems (CSPs). One way to solve a CSP instance is to encode it into SAT and use a SAT-solver. However, important information about the problem can get lost during the translation stage. For example, although the general constraint satisfaction problem is known to be NP-complete, there are some classes of CSP instances that have been shown to be tractable. These include the classes of CSP instances that contain only max-closed or connected-row-convex constraints. In this paper we show that translating such instances using some common standard encodings results in SAT instances which do not fall into known tractable classes. However, translating such instances using the order encoding results in SAT instances that do fall into known tractable classes. Moreover, modern clause learning SAT-solvers can then solve them efficiently. Hence, we give a theory-based argument to prefer the order encoding for certain families of constraint satisfaction problems.

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The Logic Behind Weighted CSP

Ansótegui

Bonet

Levy³

et al. 2007

Trends in Constraint Programming

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We define a translation from Weighted CSP to signed Max-SAT, and a complete resolution-style calculus for solving signed Max-SAT. Based on these results, we then describe an original exact algorithm for solving Weighted CSP. Finally, we define several derived rules and prove that they enforce the main soft arc consistency defined in the literature when applied to Weighted CSP instances. * This research was founded by the MEC research projects iDEAS (TIN2004-04343), Mulog (TIN2004-07933-C03-01/03) and SofSAT (TIC2003-00950), and the program Ramón y Cajal.

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Mapping Problems with Finite-Domain Variables to Problems with Boolean Variables

Cited by 60 publications

References 14 publications

Towards Robust CNF Encodings of Cardinality Constraints

Towards Robust CNF Encodings of Cardinality Constraints

The Order Encoding: From Tractable CSP to Tractable SAT

The Logic Behind Weighted CSP

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