{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7506","name":"Chordal Editing is Fixed-Parameter Tractable","abstract":"Graph modification problems are typically asked as follows: is there a set of k operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly different versions by allowing different operations. We study a very general graph modification problem which allows all three types of operations: given a graph G and integers k_1, k_2, and k_3, the CHORDAL EDITING problem asks if G can be transformed into a chordal graph by at most k_1 vertex deletions, k_2 edge deletions, and k_3 edge additions. Clearly, this problem generalizes both CHORDAL VERTEX\/EDGE DELETION and CHORDAL COMPLETION (also known as MINIMUM FILL-IN). Our main result is an algorithm for CHORDAL EDITING in time 2^O(k.log(k))\u00b7n^O(1), where k:=k_1+k_2+k_3; therefore, the problem is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm is both more efficient and conceptually simpler than the previously known algorithm for the special case CHORDAL DELETION.","keywords":["chordal graph","parameterized computation","graph modification problems","chordal deletion","chordal completion","clique tree decomposition","holes","simplic"],"author":[{"@type":"Person","name":"Cao, Yixin","givenName":"Yixin","familyName":"Cao"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"position":20,"pageStart":214,"pageEnd":225,"dateCreated":"2014-03-05","datePublished":"2014-03-05","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Cao, Yixin","givenName":"Yixin","familyName":"Cao"},{"@type":"Person","name":"Marx, D\u00e1niel","givenName":"D\u00e1niel","familyName":"Marx"}],"copyrightYear":"2014","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2014.214","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6228","volumeNumber":25,"name":"31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)","dateCreated":"2014-03-05","datePublished":"2014-03-05","editor":[{"@type":"Person","name":"Mayr, Ernst W.","givenName":"Ernst W.","familyName":"Mayr"},{"@type":"Person","name":"Portier, Natacha","givenName":"Natacha","familyName":"Portier"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7506","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":"#volume6228"}}}