Approximation and Exact Algorithms for Constructing Minimum Ultrametric Trees from Distance Matrices

  • Bang Ye Wu
  • Kun-Mao Chao
  • Chuan Yi Tang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)


Constructing minimum ultrametric trees from distance matrices is an important problem in computational biology. In this paper, we examine its computational complexity and approximability. When the distances satisfy the triangle inequalities, we show that the minimum ultrametric tree problem can be approximated in polynomial time with error ratio 1.5(1 + ⌈log n⌉), where n is the number of species. We also developed an efficient branch and bound algorithm for constructing the minimum ultrametric tree for both metric and nonmetric inputs. The experimental results show that it can find an optimal solution for 25 species within reasonable time, while, to the best of our knowledge, there is no report of algorithms solving the problem even for 12 species.


computational biology ultrametric trees approximation algorithms branch and bound 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bang Ye Wu
    • 1
  • Kun-Mao Chao
    • 2
  • Chuan Yi Tang
    • 1
  1. 1.Dept. of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan, R.O.C.
  2. 2.Dept. of Computer Science and Information ManagementProvidence UniversityShaluTaiwan, R.O.C.

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