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)


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.


Approximation Algorithm Branch Point Internal Node Approximation Phase Input Tree 
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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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