Generalized Totalizer Encoding for PseudoBoolean Constraints
Abstract
PseudoBoolean constraints, also known as 01 Integer Linear Constraints, are used to model many realworld problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudoBoolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), which is an arcconsistency preserving extension of the Totalizer encoding to pseudoBoolean constraints. Unlike some other encodings, the number of auxiliary variables required for GTE does not depend on the magnitudes of the coefficients. Instead, it depends on the number of distinct combinations of these coefficients. We show the superiority of GTE with respect to other encodings when large pseudoBoolean constraints have low number of distinct coefficients. Our experimental results also show that GTE remains competitive even when the pseudoBoolean constraints do not have this characteristic.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 arXiv:
 arXiv:1507.05920
 Bibcode:
 2015arXiv150705920J
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Artificial Intelligence
 EPrint:
 10 pages, 2 figures, 2 tables. To be published in 21st International Conference on Principles and Practice of Constraint Programming 2015