{"type":"ScholarlyArticle","title":"A SAT Approach to Branchwidth","authors":[{"name":"Neha Lodha","slug":"neha-lodha","given":"Neha","family":"Lodha","affiliation":"Algorithms and Complexity Group , TU Wien , Austria"},{"name":"Sebastian Ordyniak","slug":"sebastian-ordyniak","given":"Sebastian","family":"Ordyniak","affiliation":"Algorithms and Complexity Group , TU Wien , Austria"},{"name":"Stefan Szeider","slug":"stefan-szeider","given":"Stefan","family":"Szeider","affiliation":"Algorithms and Complexity Group , TU Wien , Austria"}],"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 develop a novel partition-based characterization of branch decompositions. 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 develop 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.","doi":"10.24963/ijcai.2017/689","url":"https://ijcai.org/proceedings/2017/689","pdf":"https://ijcai.org/proceedings/2017/0689.pdf","markdown":"https://ijcai.org/proceedings/2017/689.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/689","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Best Sister Conferences","track":"Best Sister Conferences","number":689,"pages":{"first":4894,"last":4898},"keywords":["Artificial Intelligence: knowledge representation and reasoning","Artificial Intelligence: other","Artificial Intelligence: search and constraint satisfaction"],"videos":[],"references":[{"position":1,"raw":"[Alekhnovich and Razborov, 2002] Michael Alekhnovich and Alexander A. 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