New Fixed-Parameter Algorithms for the Minimum Quartet Inconsistency Problem

  • Authors:

  • Maw-Shang Chang;Chuang-Chieh Lin;Peter Rossmanith

  • Affiliations:

  • National Chung Cheng University, Department of Computer Science and Information Engineering, 621, Ming-Hsiung, Chiayi, Taiwan;National Chung Cheng University, Department of Computer Science and Information Engineering, 621, Ming-Hsiung, Chiayi, Taiwan;RWTH Aachen University, Department of Computer Science, Ahornstr. 55, 52056, Aachen, Germany

  • Venue:
  • Theory of Computing Systems
  • Year:
  • 2010

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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 ε0 is an arbitrarily small constant.