Algorithmica

, Volume 25, Issue 2, pp 176–195

On the Linear-Cost Subtree-Transfer Distance between Phylogenetic Trees

  • B. DasGupta
  • X. He
  • T. Jiang
  • M. Li
  • J. Tromp

DOI: 10.1007/PL00008273

Cite this article as:
DasGupta, B., He, X., Jiang, T. et al. Algorithmica (1999) 25: 176. doi:10.1007/PL00008273

Abstract.

Different phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [16] or from different genes [12] in the study of molecular evolution. Comparing these trees to find their similarities and dissimilarities (i.e., distance ) is thus an important issue in computational molecular biology. Several distance metrics including the nearest neighbor interchange (nni) distance and the subtree-transfer distance have been proposed and extensively studied in the literature. This article considers a natural extension of the subtree-transfer distance, called the linear-cost subtree-transfer distance, and studies the complexity and efficient approximation algorithms for this distance as well as its relationship to the nni distance. The linear-cost subtree-transfer model seems more suitable than the (unit-cost) subtree-transfer model in some applications. The following is a list of our results:

1. The linear-cost subtree-transfer distance is in fact identical to the nni distance on unweighted phylogenies.

2. There is an algorithm to compute an optimal linear-cost subtree-transfer sequence between unweighted phylogenies in O(n2O(d)) time, where d denotes the linear-cost subtree-transfer distance. Such an algorithm is useful when d is small.

3. Computing the linear-cost subtree-transfer distance between two weighted phylogenetic trees is NP-hard, provided we allow multiple leaves of a tree to share the same label (i.e., the trees are not necessarily uniquely labeled).

4. There is an efficient approximation algorithm for computing the linear-cost subtree-transfer distance between weighted phylogenies with performance ratio 2 .

Key words. Evolutionary trees, Approximation algorithms, Lower bounds. 

Copyright information

© 1999 Springer-Verlag New York Inc.

Authors and Affiliations

  • B. DasGupta
    • 1
  • X. He
    • 2
  • T. Jiang
    • 3
  • M. Li
    • 4
  • J. Tromp
    • 5
  1. 1.Department of Computer Science, Rutgers University, Camden, NJ 08102, USA. bhaskar@crab.rutgers.edu.US
  2. 2.Department of Computer Science, SUNY-Buffalo, Buffalo, NY 14260, USA. xinhe@cs.buffalo.edu.US
  3. 3.Department of Computer Science, McMaster University, Hamilton, Ontario, Canada L8S 4K1. jiang@maccs.mcmaster.ca.CA
  4. 4.Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. mli@math.uwaterloo.ca.CA
  5. 5.CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. tromp@cwi.nl.NL