 License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2017.65
URN: urn:nbn:de:0030-drops-81100
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8110/
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### An Improved FPT Algorithm for the Flip Distance Problem

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### Abstract

Given a set \cal P of points in the Euclidean plane and two triangulations of \cal P, the flip distance between these two triangulations is the minimum number of flips required to transform one triangulation into the other. The Parameterized Flip Distance problem is to decide if the flip distance between two given triangulations is equal to a given integer k. The previous best FPT algorithm runs in time O^*(k\cdot c^k) (c\leq 2\times 14^11), where each step has fourteen possible choices, and the length of the action sequence is bounded by 11k. By applying the backtracking strategy and analyzing the underlying property of the flip sequence, each step of our algorithm has only five possible choices. Based on an auxiliary graph G, we prove that the length of the action sequence for our algorithm is bounded by 2|G|. As a result, we present an FPT algorithm running in time O^*(k\cdot 32^k).

### BibTeX - Entry

@InProceedings{li_et_al:LIPIcs:2017:8110,
author =	{Shaohua Li and Qilong Feng and Xiangzhong Meng and Jianxin Wang},
title =	{{An Improved FPT Algorithm for the Flip Distance Problem}},
booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
pages =	{65:1--65:13},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-046-0},
ISSN =	{1868-8969},
year =	{2017},
volume =	{83},
editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8110},
URN =		{urn:nbn:de:0030-drops-81100},
doi =		{10.4230/LIPIcs.MFCS.2017.65},
annote =	{Keywords: triangulation, flip distance, FPT algorithm}
}


 Keywords: triangulation, flip distance, FPT algorithm Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) Issue Date: 2017 Date of publication: 01.12.2017

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