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On the complexity of comparing evolutionary trees

Extended abstract
  • Jotun Hein
  • Tao Jiang
  • Lusheng Wang
  • Kaizhong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 937)

Abstract

We study the computational complexity and approximation of several problems arising in the comparison of evolutionary trees. It is shown that the maximum agreement subtree (MAST) problem for three trees with unbounded degree cannot be approximated within ratio \(2^{\log ^\delta n}\)in polynomial time for any δ < 1, unless NP \(\subseteq\)DTIME[2polylog n], and MAST with edge contractions for two binary trees is NP-hard. This answers two open questions posed in [1]. For the maximum refinement subtree (MRST) problem involving two trees, we show that it is polynomialtime solvable when both trees have bounded degree and is NP-hard when one of the trees can have an arbitrary degree. Finally, we consider the problem of optimally transforming a tree into another by transferring subtrees around. It is shown that computing the subtree-transfer distance is NP-hard and an approximation algorithm with performance ratio 3 is given.

Keywords

Internal Node Evolutionary Tree Arbitrary Degree Edge Contraction Exact Cover 
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 1995

Authors and Affiliations

  • Jotun Hein
    • 1
  • Tao Jiang
    • 2
  • Lusheng Wang
    • 3
  • Kaizhong Zhang
    • 4
  1. 1.Institute for Genetics and EcologyAarhus UniversityDenmark
  2. 2.Department of Computer ScienceMcMaster UniversityHamiltonCanada
  3. 3.Department of Electrical and Computer EngineeringMcMaster UniversityHamiltonCanada
  4. 4.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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