{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8200","name":"Maximum Matching Width: New Characterizations and a Fast Algorithm for Dominating Set","abstract":"We give alternative definitions for maximum matching width, e.g., a graph G has mmw(G) <= k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A,B,C \\subseteq X with A \\cup B \\cup C=X and |A|,|B|,|C| <= k such that any subset of X that is a minimal separator of H is a subset of either A, B or C. Treewidth and branchwidth have alternative definitions through intersections of subtrees, where treewidth focuses on nodes and branchwidth focuses on edges. We show that mm-width combines both aspects, focusing on nodes and on edges. Based on this we prove that given a graph G and a branch decomposition of mm-width k we can solve Dominating Set in time O^*(8^k), thereby beating O^*(3^{tw(G)}) whenever tw(G) > log_3(8) * k ~ 1.893 k. Note that mmw(G) <= tw(G)+1 <= 3 mmw(G) and these inequalities are tight. Given only the graph G and using the best known algorithms to find decompositions, maximum matching width will be better for solving Dominating Set whenever tw(G) > 1.549 * mmw(G).","keywords":["FPT algorithms","treewidth","dominating set"],"author":[{"@type":"Person","name":"Jeong, Jisu","givenName":"Jisu","familyName":"Jeong"},{"@type":"Person","name":"S\u00e6ther, Sigve Hortemo","givenName":"Sigve Hortemo","familyName":"S\u00e6ther"},{"@type":"Person","name":"Telle, Jan Arne","givenName":"Jan Arne","familyName":"Telle"}],"position":18,"pageStart":212,"pageEnd":223,"dateCreated":"2015-11-19","datePublished":"2015-11-19","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Jeong, Jisu","givenName":"Jisu","familyName":"Jeong"},{"@type":"Person","name":"S\u00e6ther, Sigve Hortemo","givenName":"Sigve Hortemo","familyName":"S\u00e6ther"},{"@type":"Person","name":"Telle, Jan Arne","givenName":"Jan Arne","familyName":"Telle"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.IPEC.2015.212","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6246","volumeNumber":43,"name":"10th International Symposium on Parameterized and Exact Computation (IPEC 2015)","dateCreated":"2015-11-19","datePublished":"2015-11-19","editor":[{"@type":"Person","name":"Husfeldt, Thore","givenName":"Thore","familyName":"Husfeldt"},{"@type":"Person","name":"Kanj, Iyad","givenName":"Iyad","familyName":"Kanj"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8200","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6246"}}}