New fixed-parameter algorithms for the minimum quartet inconsistency problem

Abstract

Given a set of n taxa S, exactly one topology for every subset of four taxa, and a positive integer k as the parameter, 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 + n4). In this paper, first we present an O(3.0446k n + n 4) algorithm and an O(2.0162 k n 3 + n 5) algorithm. Finally, we give an O*((1 + ε) k ) algorithm with an arbitrarily small constant ε > 0. © 2008 Springer-Verlag Berlin Heidelberg.