New fixed-parameter algorithms for the minimum quartet inconsistency problem

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Title:	New fixed-parameter algorithms for the minimum quartet inconsistency problem
Authors:	Chang, Maw-Shang;Lin, Chuang-Chieh;Rossmanith, Peter
Keywords:	Evolutionary tree;Quartet topology;Leaf-labeled tree;Minimum quartet inconsistency problem;Fixed-parameter algorithm;Depth-bounded search tree
Date:	2009-01-27
Issue Date:	2021-03-05 12:12:48 (UTC+8)
Abstract:	Let S be a set of n taxa. Given a parameter k and a set of quartet topologies Q over S such that there is exactly one topology for every subset of four taxa, the parameterized Minimum Quartet Inconsistency (MQI) problem is to decide whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in at most k quartet topologies. The best fixed-parameter algorithm devised so far for the parameterized MQI problem runs in time O(4k n+n 4). In this paper, first we present an O(3.0446k n+n 4) fixed-parameter algorithm and an O(2.0162k n 3+n 5) fixed-parameter algorithm for the parameterized MQI problem. Finally, we give an O *((1+ε)k) fixed-parameter algorithm, where ε>0 is an arbitrarily small constant.
Relation:	Theory of Computing Systems 47, pp.342–367
DOI:	10.1007/s00224-009-9165-y
Appears in Collections:	[Graduate Institute & Department of Computer Science and Information Engineering] Journal Article

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