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A SAT Approach to Branchwidth

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9710)

Abstract

Branch decomposition is a prominent method for structurally decomposing a graph, hypergraph or CNF formula. The width of a branch decomposition provides a measure of how well the object is decomposed. For many applications it is crucial to compute a branch decomposition whose width is as small as possible. We propose a SAT approach to finding branch decompositions of small width. The core of our approach is an efficient SAT encoding which determines with a single SAT-call whether a given hypergraph admits a branch decomposition of certain width. For our encoding we developed a novel partition-based characterization of branch decomposition. The encoding size imposes a limit on the size of the given hypergraph. In order to break through this barrier and to scale the SAT approach to larger instances, we developed a new heuristic approach where the SAT encoding is used to locally improve a given candidate decomposition until a fixed-point is reached. This new method scales now to instances with several thousands of vertices and edges.

Notes

Acknowledgement

We thank Illya Hicks for providing us the code of his branchwidth heuristics and acknowledge support by the Austrian Science Fund (FWF, projects W1255-N23 and P-27721).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Neha Lodha
    • 1
  • Sebastian Ordyniak
    • 1
  • Stefan Szeider
    • 1
  1. 1.Algorithms and Complexity GroupTU WienViennaAustria

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