Perfect hashing and CNF encodings of cardinality constraints

Authors:
Yael Ben-Haim;Alexander Ivrii;Oded Margalit;Arie Matsliah
Affiliations:
IBM R&D Labs in Israel, Haifa, Israel;IBM R&D Labs in Israel, Haifa, Israel;IBM R&D Labs in Israel, Haifa, Israel;IBM R&D Labs in Israel, Haifa, Israel
Venue:
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Year:
2012

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Abstract

We study the problem of encoding cardinality constraints (threshold functions) on Boolean variables into CNF. Specifically, we propose new encodings based on (perfect) hashing that are efficient in terms of the number of clauses, auxiliary variables, and propagation strength. We compare the properties of our encodings to known ones, and provide experimental results evaluating their practical effectiveness.