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Towards an optimal CNF encoding of Boolean cardinality constraints

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Carsten SinzAuthors Info & Claims

CP'05: Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming

Pages 827 - 831

https://doi.org/10.1007/11564751_73

Published: 01 October 2005 Publication History

Abstract

We consider the problem of encoding Boolean cardinality constraints in conjunctive normal form (CNF). Boolean cardinality constraints are formulae expressing that at most (resp. at least) k out of n propositional variables are true. We give two novel encodings that improve upon existing results, one which requires only 7n clauses and 2n auxiliary variables, and another one demanding O(n·k) clauses, but with the advantage that inconsistencies can be detected in linear time by unit propagation alone. Moreover, we prove a linear lower bound on the number of required clauses for any such encoding.

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CP'05: Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming

October 2005

883 pages

ISBN:9783540292388

Editor:
Peter van Beek
Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 October 2005

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Towards robust CNF encodings of cardinality constraints

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