Modulo Based CNF Encoding of Cardinality Constraints and Its Application to MaxSAT Solvers

Ogawa, Toru; Liu, Yangyang; Hasegawa, Ryuzo; Koshimura, Miyuki; Fujita, Hiroshi

doi:10.1109/ictai.2013.13

Cited by 23 publications

(21 citation statements)

References 10 publications

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“…A cardinality constraint of the form x i ≤ k is referred to as an AtMostk constraint, whereas a cardinality constraint of the form x i ≥ k is referred to as an AtLeastk constraint. The study of propositional encodings of cardinality and pseudo-Boolean constraints is an area of active research [1,4,5,9,10,17,25,34,58,65,69].…”

Section: Preliminariesmentioning

confidence: 99%

On Tackling the Limits of Resolution in SAT Solving

Ignatiev

Morgado

Marques-Silva

2017

Theory and Applications of Satisfiability Testing – SAT 2017

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Abstract. The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers.

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Section: Preliminariesmentioning

confidence: 99%

On Tackling the Limits of Resolution in SAT Solving

Ignatiev

Morgado

Marques-Silva

2017

Theory and Applications of Satisfiability Testing – SAT 2017

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“…+ l n ≤ k into a set of clauses. MSCG uses different cardinality constraints encodings, in particular in this work we consider the Bitwise encoding [12] (for which k = 1), a variant of the Modulo Totalizer encoding [11], the Totalizer encoding [2] (these correspond to the encodings used by MSCG in the MaxSAT Evaluation 2014) and its iterative version [6].…”

Section: Cardinality Constraint Encodingsmentioning

confidence: 99%

“…The idea of the variant of the Modulo Totalizer is to use the Modulo Totalizer encoding but approximating it to the technique of k-cardinality. This variant was motivated by the proposed future work in the Conclusions section of [11], where their goal is to do kcardinality of the Modulo Totalizer instead of approximating it.…”

Section: Cardinality Constraint Encodingsmentioning

confidence: 99%

MSCG: Robust Core-Guided MaxSAT Solving

Morgado

Ignatiev²,

Marques-Silva

2015

SAT

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“…For the purpose of this paper, we describe the Totalizer encoding [10] for cardinality constraints, as later in the paper we build upon this encoding to present iterative encoding. However, other effective alternative encodings for cardinality constraints exist [54,8,51].…”

Section: Totalizer Encodingmentioning

confidence: 99%

On Using Incremental Encodings in Unsatisfiability-based MaxSAT Solving

Martins

Joshi

Manquinho

et al. 2015

SAT

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In recent years, unsatisfiability-based algorithms have become prevalent as state of the art for solving industrial instances of Maximum Satisfiability (MaxSAT). These algorithms perform a succession of unsatisfiable SAT solver calls until an optimal solution is found. In several of these algorithms, cardinality or pseudo-Boolean constraints are extended between iterations. However, in most cases, the formula provided to the SAT solver in each iteration must be rebuilt and no knowledge is reused from one iteration to the next. This paper describes how to implement incremental unsatisfiability-based algorithms for MaxSAT. In particular, we detail and analyze our implementation of the MSU3 algorithm in the open-wbo framework that performed remarkably well in the MaxSAT Evaluation of 2014. Furthermore, we also propose to extend incrementality to weighted MaxSAT through an incremental encoding of pseudo-Boolean constraints. The experimental results show that the performance of MaxSAT algorithms can be greatly improved by exploiting the learned information and maintaining the internal state of the SAT solver between iterations. Finally, the proposed incremental encodings of cardinality and pseudo-Boolean constraints are not exclusive for MaxSAT usage and can be used in other domains.

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Modulo Based CNF Encoding of Cardinality Constraints and Its Application to MaxSAT Solvers

Cited by 23 publications

References 10 publications

On Tackling the Limits of Resolution in SAT Solving

On Tackling the Limits of Resolution in SAT Solving

MSCG: Robust Core-Guided MaxSAT Solving

On Using Incremental Encodings in Unsatisfiability-based MaxSAT Solving

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