Incremental Encoding and Solving of Cardinality Constraints

  • Sven Reimer
  • Matthias Sauer
  • Tobias Schubert
  • Bernd Becker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8837)


Traditional SAT-based MaxSAT solvers encode cardinality constraints directly as part of the CNF and solve the entire optimization problem by a sequence of iterative calls of the underlying SAT solver. The main drawback of such approaches is their dependence on the number of soft clauses: The more soft clauses the MaxSAT instance contains, the larger is the CNF part encoding the cardinality constraints. To counter this drawback, we introduce an innovative encoding of cardinality constraints: Instead of translating the entire and probably bloated constraint network into CNF, a divide-and-conquer approach is used to encode partial constraint networks successively. The resulting subproblems are solved and merged incrementally, reusing not only intermediate local optima, but also additional constraints which are derived from solving the individual subproblems by the back-end SAT solver. Extensive experimental results for the last MaxSAT evaluation benchmark suitew demonstrate that our encoding is in general smaller compared to existing methods using a monolithic encoding of the constraints and converges faster to the global optimum.


Conjunctive Normal Form Cardinality Constraint Unit Clause Sorting Network Relaxation Variable 
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 2014

Authors and Affiliations

  • Sven Reimer
    • 1
  • Matthias Sauer
    • 1
  • Tobias Schubert
    • 1
  • Bernd Becker
    • 1
  1. 1.Institute of Computer ScienceAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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