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.
Dedicated to the memory of Helmuth Veith (1971–2016).
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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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Lodha, N., Ordyniak, S., Szeider, S. (2016). A SAT Approach to Branchwidth. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_12
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DOI: https://doi.org/10.1007/978-3-319-40970-2_12
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