{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7263","name":"Directed Acyclic Subgraph Problem Parameterized above the Poljak-Turzik Bound","abstract":"An oriented graph is a directed graph without directed 2-cycles. Poljak and Turzik (1986) proved that every connected oriented graph G on n vertices and m arcs contains an acyclic subgraph with at least m\/2+(n-1)\/4 arcs. Raman and Saurabh (2006) gave another proof of this result and left it as an open question to establish the parameterized complexity of the following problem: does G have an acyclic subgraph with least m\/2 + (n-1)\/4 + k arcs, where k is the parameter? We answer this question by showing that the problem can be solved by an algorithm of runtime (12k)!n^{O(1)}. Thus, the problem is fixed-parameter tractable. We also prove that there is a polynomial time algorithm that either establishes that the input instance of the problem is a Yes-instance or reduces the input instance to an equivalent one of size O(k^2).","keywords":["Acyclic Subgraph","Fixed-parameter tractable","Polynomial Kernel"],"author":[{"@type":"Person","name":"Crowston, Robert","givenName":"Robert","familyName":"Crowston"},{"@type":"Person","name":"Gutin, Gregory","givenName":"Gregory","familyName":"Gutin"},{"@type":"Person","name":"Jones, Mark","givenName":"Mark","familyName":"Jones"}],"position":36,"pageStart":400,"pageEnd":411,"dateCreated":"2012-12-14","datePublished":"2012-12-14","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Crowston, Robert","givenName":"Robert","familyName":"Crowston"},{"@type":"Person","name":"Gutin, Gregory","givenName":"Gregory","familyName":"Gutin"},{"@type":"Person","name":"Jones, Mark","givenName":"Mark","familyName":"Jones"}],"copyrightYear":"2012","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2012.400","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6221","volumeNumber":18,"name":"IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)","dateCreated":"2012-12-14","datePublished":"2012-12-14","editor":[{"@type":"Person","name":"D'Souza, Deepak","givenName":"Deepak","familyName":"D'Souza"},{"@type":"Person","name":"Radhakrishnan, Jaikumar","givenName":"Jaikumar","familyName":"Radhakrishnan"},{"@type":"Person","name":"Telikepalli, Kavitha","givenName":"Kavitha","familyName":"Telikepalli"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7263","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":"#volume6221"}}}