New fixed-parameter algorithms for the minimum quartet inconsistency problem

Authors:
Maw-Shang Chang;Chuang-Chieh Lin;Peter Rossmanith
Affiliations:
Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan, R.O.C.;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan, R.O.C.;Department of Computer Science, RWTH Aachen University, Germany
Venue:
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Year:
2008

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Abstract

Given a set of n taxa S, exactly one topology for every subsetof four taxa, and a positive integer k as the parameter, the parameterizedMinimum Quartet Inconsistency (MQI) problem is to decide whether wecan find an evolutionary tree inducing a set of quartet topologies thatdiffers from the given set in at most k quartet topologies. The best fixedparameteralgorithm devised so far for the parameterized MQI problemruns in time O(4kn+n4). In this paper, first we present an O(3.0446kn+n4) algorithm and an O(2.0162kn3 + n5) algorithm. Finally, we give anO*((1 + Ɛ)k) algorithm with an arbitrarily small constant Ɛ 0.