2026-07-26T01:16:09Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:4937 2024-03-06T10:35:35Z ddc:004 open_access

Flip Distance Is in FPT Time O(n+ k * c^k) Kanj, Iyad Xia, Ge triangulations flip distance parameterized algorithms 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. In this paper we present an algorithm for the Flip Distance problem that runs in time O(n + k \cdot c^{k}), for a constant c \leq 2 \cdot 14^11, which implies that the problem is fixed-parameter tractable. The NP-hardness reduction for the Flip Distance problem given by Lubiw and 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Iyad Kanj and Ge Xia 2015 Is Part Of LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2015.500 urn:nbn:de:0030-drops-49371 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.500 eng https://creativecommons.org/licenses/by/3.0/legalcode