{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article8603","name":"Extension Complexity, MSO Logic, and Treewidth","abstract":"We consider the convex hull P_phi(G) of all satisfying assignments of a given MSO_2 formula phi on a given graph G. We show that there exists an extended formulation of the polytope P_phi(G) that can be described by f(|phi|,tau)*n inequalities, where n is the number of vertices in G, tau is the treewidth of G and f is a computable function depending only on phi and tau.\r\n\r\nIn other words, we prove that the extension complexity of P_phi(G) is linear in the size of the graph G, with a constant depending on the treewidth of G and the formula phi. This provides a very general yet very simple meta-theorem about the extension complexity of polytopes related to a wide class of problems and graphs.","keywords":["Extension Complexity","FPT","Courcelle's Theorem","MSO Logic"],"author":[{"@type":"Person","name":"Kolman, Petr","givenName":"Petr","familyName":"Kolman"},{"@type":"Person","name":"Kouteck\u00fd, Martin","givenName":"Martin","familyName":"Kouteck\u00fd"},{"@type":"Person","name":"Tiwary, Hans Raj","givenName":"Hans Raj","familyName":"Tiwary"}],"position":18,"pageStart":"18:1","pageEnd":"18:14","dateCreated":"2016-06-22","datePublished":"2016-06-22","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kolman, Petr","givenName":"Petr","familyName":"Kolman"},{"@type":"Person","name":"Kouteck\u00fd, Martin","givenName":"Martin","familyName":"Kouteck\u00fd"},{"@type":"Person","name":"Tiwary, Hans Raj","givenName":"Hans Raj","familyName":"Tiwary"}],"copyrightYear":"2016","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.SWAT.2016.18","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":["http:\/\/arxiv.org\/abs\/1501.00288","http:\/\/www.optimization-online.org\/DB_HTML\/2014\/09\/4540.html"],"isPartOf":{"@type":"PublicationVolume","@id":"#volume6256","volumeNumber":53,"name":"15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)","dateCreated":"2016-06-22","datePublished":"2016-06-22","editor":{"@type":"Person","name":"Pagh, Rasmus","givenName":"Rasmus","familyName":"Pagh"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article8603","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":"#volume6256"}}}