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Approximation algorithms for the fixed-topology phylogenetic number problem

  • Mary Cryan
  • Leslie Ann Goldberg
  • Cynthia A. Phillips
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1264)

Abstract

In the ℓ-phylogeny problem, one wishes to construct an evolutionary tree for a set of species represented by characters, in which each state of each character induces no more than ℓ connected components. We consider the fixed-topology version of this problem for fixed-topologies of arbitrary degree. This version of the problem is known to be NP-complete for ℓ≥3 even for degree-3 trees in which no state labels more than ℓ+1 leaves (and therefore there is a trivial ℓ+1 phylogeny). We give a 2-approximation algorithm for all ℓ≥3 for arbitrary input topologies and we give an optimal approximation algorithm that constructs a 4-phylogeny when a 3-phylogeny exists. Dynamic programming techniques, which are typically used in fixed-toplogy problems, cannot be applied to ℓ-phylogeny problems. Our 2-approximation algorithm is the first application of linear programming to approximation algorithms for phylogeny problems. We extend our results to a related problem in which characters are polymorphic.

Keywords

Approximation Algorithm Branch Point Internal Node Approximation Phase Input Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Mary Cryan
    • 1
  • Leslie Ann Goldberg
    • 2
  • Cynthia A. Phillips
    • 3
  1. 1.Department of Computer ScienceUniversity of WarwickCoventryUK
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryUK
  3. 3.Sandia National LaboratoriesAlbuquerque

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