Generalized Totalizer Encoding for Pseudo-Boolean Constraints

  • Saurabh JoshiEmail author
  • Ruben Martins
  • Vasco Manquinho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9255)


Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world 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 pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), which is an arc-consistency preserving extension of the Totalizer encoding to pseudo-Boolean 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 pseudo-Boolean constraints have low number of distinct coefficients. Our experimental results also show that GTE remains competitive even when the pseudo-Boolean constraints do not have this characteristic.


Auxiliary Variable Boolean Modeling Cardinality Constraint Automate Test Pattern Generation Virtual Machine Consolidation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK
  2. 2.INESC-ID/Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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