Translating Pseudo-Boolean Constraints into CNF

Aavani, Amir

doi:10.1007/978-3-642-21581-0_28

Cited by 13 publications

(15 citation statements)

References 11 publications

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“…In the following, by testing the remaining graphs modulo 3, then modulo 4 and so forth, the graphs are sieved step by step. From the Chinese Remainder Theorem we can conclude the following theorem (see e.g., [1,9]). Now, let us test whether we can apply Theorem 7 to our problem of finding a TML with 11 vertices.…”

Section: Modulo-sievingmentioning

confidence: 97%

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SAT and IP based algorithms for magic labeling including a complete search for total magic labelings

Jäger

Arnold

2015

Journal of Discrete Algorithms

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Please cite this article in press as: G. Jäger, F. Arnold, SAT and IP based algorithms for magic labeling including a complete search for total magic labelings, Journal of Discrete Algorithms (2015), http://dx. AbstractIn this paper a labeling of a graph with n vertices and m edges is a oneto-one mapping from the union of the set of vertices and edges onto the set {1, 2, . . . , m+n}. Such a labeling is defined as magic, if one or both of the following two conditions is fulfilled: the sum of an edge label and the labels of its endpoint vertices is constant for all edges; the sum of a vertex label and the labels of its incident edges is constant for all vertices. If a graph has a labeling fulfilling both conditions, it is called a totally magic graph. We present effective IP and Sat based algorithms for the problem of finding a magic labeling for a given graph, and we extend these algorithms also to find all magic labelings for a given graph. We experimentally compare the resulted algorithms by applying it to random graphs. Finally, we demonstrate its performance by solving small cases of seven open problems within the theory of magic graphs. As main practical result we perform an exhaustive search showing that no totally magic graph with 11 vertices exists.

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Section: Modulo-sievingmentioning

confidence: 97%

“…, r} exists with x i,j = True. (1) Secondly, each label has to be used by exactly one edge/vertex. This leads to the condition:…”

Section: Labeling Clausesmentioning

confidence: 99%

SAT and IP based algorithms for magic labeling including a complete search for total magic labelings

Jäger

Arnold

2015

Journal of Discrete Algorithms

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“…Solver MiniSat+ have been slightly modified, namely, we fixed several bugs such as the one reported in the experiments section of [5].…”

Section: Experimental Evaluationmentioning

confidence: 99%

Encoding cardinality constraints using standard encoding of generalized selection networks preserves arc-consistency

Karpiński

2018

Theoretical Computer Science

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“…PB constraints are intensively used in expressing NP-hard problems. While there are dedicated solvers (such as Sat4j) for solving PB constraints, there are good reasons to be interested in transforming the constraints into SAT (CNF formulae), and a number of methods for doing this have been reported [53,12,36,2,55,33,1,13]. where a 1 , .…”

Section: Introductionmentioning

confidence: 99%

Solving MaxSAT by Successive Calls to a SAT Solver

Halaby¹

2017

Proceedings of SAI Intelligent Systems Conference (IntelliSys) 2016

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The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been developed during recent years, and many of them were presented in the well-known SAT conference. Algorithms for MaxSAT generally fall into two categories: (1) branch and bound algorithms and (2) algorithms that use successive calls to a SAT solver (SATbased), which this paper in on. In practical problems, SAT-based algorithms have been shown to be more efficient. This paper provides an experimental investigation to compare the performance of recent SAT-based and branch and bound algorithms on the benchmarks of the MaxSAT Evaluations.

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Translating Pseudo-Boolean Constraints into CNF

Cited by 13 publications

References 11 publications

SAT and IP based algorithms for magic labeling including a complete search for total magic labelings

SAT and IP based algorithms for magic labeling including a complete search for total magic labelings

Encoding cardinality constraints using standard encoding of generalized selection networks preserves arc-consistency

Solving MaxSAT by Successive Calls to a SAT Solver

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