Additive Approximation for Near-Perfect Phylogeny Construction

  • Pranjal Awasthi
  • Avrim Blum
  • Jamie Morgenstern
  • Or Sheffet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7408)


We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on n points over the Boolean hypercube of dimension d. It is known that an optimal tree can be found in linear time [1] if the given dataset has a perfect phylogeny, i.e. cost of the optimal phylogeny is exactly d. Moreover, if the data has a near-perfect phylogeny, i.e. the cost of the optimal Steiner tree is d + q, it is known [2] that an exact solution can be found in running time which is polynomial in the number of species and d, yet exponential in q. In this work, we give a polynomial-time algorithm (in both d and q) that finds a phylogenetic tree of cost d + O(q 2). This provides the best guarantees known—namely, a (1 + o(1))-approximation—for the case \(\log(d) \ll q \ll \sqrt{d}\), broadening the range of settings for which near-optimal solutions can be efficiently found. We also discuss the motivation and reasoning for studying such additive approximations.


Minimum Span Tree Steiner Tree Steiner Tree Problem Good Coordinate Minimum Steiner 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 2012

Authors and Affiliations

  • Pranjal Awasthi
    • 1
  • Avrim Blum
    • 1
  • Jamie Morgenstern
    • 1
  • Or Sheffet
    • 1
  1. 1.Carnegie Mellon University, PittsburghPittsburghUSA

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