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New Fixed-Parameter Algorithms for the Minimum Quartet Inconsistency Problem

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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 ε>0 is an arbitrarily small constant.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi, 621, Taiwan

    Maw-Shang Chang & Chuang-Chieh Lin

  2. Department of Computer Science, RWTH Aachen University, Ahornstr. 55, 52056, Aachen, Germany

    Peter Rossmanith

Authors
  1. Maw-Shang Chang
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  2. Chuang-Chieh Lin
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  3. Peter Rossmanith
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Correspondence to Chuang-Chieh Lin.

Additional information

This research was supported by NSC-DAAD Sandwich Program and partially supported by the National Science Council of Taiwan under grant no. NSC 96-2221-E-194-045-MY3, and was carried out at RWTH Aachen University, Germany. A preliminary version of this paper appeared in the Proceedings of the 3rd International Workshop on Parameterized and Exact Computation (IWPEC), Lecture Notes in Computer Science, vol. 5018, pp. 66–77.

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Chang, MS., Lin, CC. & Rossmanith, P. New Fixed-Parameter Algorithms for the Minimum Quartet Inconsistency Problem. Theory Comput Syst 47, 342–367 (2010). https://doi.org/10.1007/s00224-009-9165-y

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  • DOI: https://doi.org/10.1007/s00224-009-9165-y

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