Using Semi-definite Programming to Enhance Supertree Resolvability

  • Shlomo Moran
  • Satish Rao
  • Sagi Snir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3692)


Supertree methods are used to construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Since accurate reconstruction methods are currently limited to a maximum of few dozens of taxa, the use of a supertree method in order to construct the tree of life is inevitable.

Supertree methods are broadly divided according to the input trees: When the input trees are unrooted, the basic reconstruction unit is a quartet tree. In this case, the basic decision problem of whether there exists a tree that agrees with all quartets is NP-complete. On the other hand, when the input trees are rooted, the basic reconstruction unit is a rooted triplet, and the above decision problem has a polynomial time algorithm. However, when there is no tree which agrees with all triplets, it would be desirable to find the tree that agrees with the maximum number of triplets. However, this optimization problem was shown to be NP-hard. Current heuristic approaches perform mincut on a graph representing the triplets inconsistency and return a tree that is guaranteed to satisfy some required properties.

In this work we present a different heuristic approach that guarantees the properties provided by the current methods and give experimental evidence that it significantly outperforms currently used methods. This method is based on divide and conquer where we use a semi-definite programming approach in the divide step.


Connectivity Graph Internal Vertex Input Tree Good Edge Parsimony Score 
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 2005

Authors and Affiliations

  • Shlomo Moran
    • 1
  • Satish Rao
    • 2
  • Sagi Snir
    • 3
  1. 1.Computer Science dept.TechnionHaifaIsrael
  2. 2.Computer Science dept.University of CaliforniaBerkeleyUSA
  3. 3.Mathematics dept.University of CaliforniaBerkeleyUSA

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