Note: Optimizing tree and character compatibility across several phylogenetic trees

  • Authors:

  • Simone Linz;Katherine St. John;Charles Semple

  • Affiliations:

  • Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand and Center for Bioinformatics, University of Tübingen, Germany;Department of Mathematics and Computer Science, Lehman College, City University of New York, Bronx, NY, United States;Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

Given a set R of rooted phylogenetic trees on overlapping taxa, it takes polynomial time to decide whether or not there exists a rooted phylogenetic tree that is compatible with R. Since not all evolutionary histories for a set of species can be explained by a single tree, it is natural to ask for the minimum number of rooted phylogenetic trees needed such that each tree in R is compatible with at least one tree. This paper shows that it is computationally hard to compute this minimum number. In particular, if R contains rooted triples (rooted binary phylogenetic trees on three leaves), it is NP-complete to decide whether there exist two rooted phylogenetic trees such that each rooted triple in R is compatible with at least one of the two trees. Furthermore, for a set @S of binary characters and a positive integer k, we show that to decide if there exists a set P of k rooted phylogenetic trees such that each character in @S is compatible with at least one tree in P is NP-complete for all k=3, but solvable in polynomial time for k=2. This generalizes the result for k=1, where it is well-known to be polynomial time.