An improved algorithm for the maximum agreement subtree problem

  • Authors:

  • Chuan-Min Lee;Ling-Ju Hung;Maw-Shang Chang;Chia-Ben Shen;Chuan-Yi Tang

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi 621, Taiwan, R.O.C.;Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi 621, Taiwan, R.O.C.;Department of Computer Science and Information Engineering, National Chung Cheng University, Ming-Hsiung, Chiayi 621, Taiwan, R.O.C.;Department of Computer Science, National Tsing Hua University, Hsin-Chu 300, Taiwan, R.O.C.;Department of Computer Science, National Tsing Hua University, Hsin-Chu 300, Taiwan, R.O.C.

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

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Abstract

In this paper, we solve the maximum agreement subtree problem for a set T of k rooted leaf-labeled evolutionary trees on n leaves where T contains a binary tree. We show that the O(kn^3)-time dynamic-programming algorithm proposed by Bryant [Building trees, hunting for trees, and comparing trees: theory and methods in phylogenetic analysis, Ph.D. thesis, Dept. Math., University of Canterbury, 1997, pp. 174-182] can be implemented in O(kn^2+n^2log^k^-^2nloglogn) and O(kn^3^-^1^/^(^k^-^1^)) time by using multidimensional range search related data structures proposed by Gabow et al. [Scaling and related techniques for geometry problems, in: Proc. 16th Annual ACM Symp. on Theory of Computing, 1984, pp. 135-143] and Bentley [Multidimensional binary search trees in database applications, IEEE Trans. Softw. Eng. SE-5 (4) (1979) 333-340], respectively. When k