2026-08-07T20:31:56Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6945 2024-03-06T10:38:50Z ddc:004 open_access

Cut and Count and Representative Sets on Branch Decompositions Pino, Willem J. A. Bodlaender, Hans L. van Rooij, Johan M. M. Graph algorithms Branchwidth Treewidth Dynamic Programming Planar Graphs Recently, new techniques have been introduced to speed up dynamic programming algorithms on tree decompositions for connectivity problems: the 'Cut and Count' method and a method called the rank-based approach, based on representative sets and Gaussian elimination. These methods respectively give randomised and deterministic algorithms that are single exponential in the treewidth, and polynomial, respectively linear in the number of vertices. In this paper, we adapt these methods to branch decompositions yielding algorithms, both randomised and deterministic, that are in many cases faster than when tree decompositions would be used. In particular, we obtain the currently fastest randomised algorithms for several problems on planar graphs. When the involved weights are O(n^{O(1)}), we obtain faster randomised algorithms on planar graphs for Steiner Tree, Connected Dominating Set, Feedback Vertex Set and TSP, and a faster deterministic algorithm for TSP. When considering planar graphs with arbitrary real weights, we obtain faster deterministic algorithms for all four mentioned problems. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Willem J. A. Pino and Hans L. Bodlaender and Johan M. M. van Rooij 2017 Is Part Of LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.IPEC.2016.27 urn:nbn:de:0030-drops-69450 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.27 eng https://creativecommons.org/licenses/by/3.0/legalcode