A fixed-parameter algorithm for minimum quartet inconsistency

  • Authors:

  • Jens Gramm;Rolf Niedermeier

  • Affiliations:

  • Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany;Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076 Tübingen, Germany

  • Venue:
  • Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
  • Year:
  • 2003

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Abstract

Given n taxa, exactly one topology for every subset of four taxa, and a positive integer k (the parameter), the MINIMUM QUARTET INCONSISTENCY (MQI) problem is the question whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in only k quartet topologies. The more general problem where we are not necessarily given a topology for every subset of four taxa appears to be fixed-parameter intractable. For MQI, however, which is also NP-complete, we can compute the required tree in time O(4kn + n4). This means that the problem is fixed-parameter tractable and that in the case of a small number k of "errors" the tree reconstruction can be done efficiently. In particular, for minimal k, our algorithm can produce all solutions that resolve k errors. Additionally, we discuss significant heuristic improvements. Experiments underline the practical relevance of our solutions.