{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7741","name":"Flip Distance Is in FPT Time O(n+ k * c^k)","abstract":"Let T be a triangulation of a set P of n points in the plane, and let e be an edge shared by two triangles in T such that the quadrilateral Q formed by these two triangles is convex. A flip of e is the operation of replacing e by the other diagonal of Q to obtain a new triangulation of P from T. The flip distance between two triangulations of P is the minimum number of flips needed to transform one triangulation into the other. The Flip Distance problem asks if the flip distance between two given triangulations of P is k, for some given k \\in \\mathbb{N}. It is a fundamental and a challenging problem.\r\n\r\nIn this paper we present an algorithm for the Flip Distance problem that\r\nruns in time O(n + k \\cdot c^{k}), for a constant c \\leq 2 \\cdot\r\n14^11, which implies that the problem is fixed-parameter tractable. The\r\nNP-hardness reduction for the Flip Distance problem given by Lubiw\r\nand Pathak can be used to show that, unless the exponential-time hypothesis (ETH) fails, the Flip Distance problem cannot be solved in time O^*(2^o(k)). Therefore, one cannot expect an asymptotic improvement in the exponent of the running time of our algorithm.","keywords":["triangulations","flip distance","parameterized algorithms"],"author":[{"@type":"Person","name":"Kanj, Iyad","givenName":"Iyad","familyName":"Kanj"},{"@type":"Person","name":"Xia, Ge","givenName":"Ge","familyName":"Xia"}],"position":42,"pageStart":500,"pageEnd":512,"dateCreated":"2015-02-26","datePublished":"2015-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kanj, Iyad","givenName":"Iyad","familyName":"Kanj"},{"@type":"Person","name":"Xia, Ge","givenName":"Ge","familyName":"Xia"}],"copyrightYear":"2015","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2015.500","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6233","volumeNumber":30,"name":"32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)","dateCreated":"2015-02-26","datePublished":"2015-02-26","editor":[{"@type":"Person","name":"Mayr, Ernst W.","givenName":"Ernst W.","familyName":"Mayr"},{"@type":"Person","name":"Ollinger, Nicolas","givenName":"Nicolas","familyName":"Ollinger"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7741","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":"#volume6233"}}}