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Community Structure Inspired Algorithms for SAT and #SAT

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Book cover Theory and Applications of Satisfiability Testing -- SAT 2015 (SAT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9340))

Abstract

We introduce h-modularity, a structural parameter of CNF formulas, and present algorithms that render the decision problem SAT and the model counting problem #SAT fixed-parameter tractable when parameterized by h-modularity. The new parameter is defined in terms of a partition of clauses of the given CNF formula into strongly interconnected communities which are sparsely interconnected with each other. Each community forms a hitting formula, whereas the interconnections between communities form a graph of small treewidth. Our algorithms first identify the community structure and then use them for an efficient solution of SAT and #SAT, respectively. We further show that h-modularity is incomparable with known parameters under which SAT or #SAT is fixed-parameter tractable.

Supported by the Austrian Science Fund (FWF), project P26696.

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Authors and Affiliations

  1. Algorithms and Complexity Group, TU Wien, Vienna, Austria

    Robert Ganian & Stefan Szeider

Authors
  1. Robert Ganian
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  2. Stefan Szeider
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Correspondence to Robert Ganian .

Editor information

Editors and Affiliations

  1. Algorithms, University of Texas, Austin, Texas, USA

    Marijn Heule

  2. Trusted Systems Research Group, Fort Meade, Texas, USA

    Sean Weaver

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Ganian, R., Szeider, S. (2015). Community Structure Inspired Algorithms for SAT and #SAT. In: Heule, M., Weaver, S. (eds) Theory and Applications of Satisfiability Testing -- SAT 2015. SAT 2015. Lecture Notes in Computer Science(), vol 9340. Springer, Cham. https://doi.org/10.1007/978-3-319-24318-4_17

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  • DOI: https://doi.org/10.1007/978-3-319-24318-4_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24317-7

  • Online ISBN: 978-3-319-24318-4

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