On the Complexity of Constructing Evolutionary Trees

Leszek Ga̧sieniec, Jesper Andreas Jansson, Andrzej Lingas, Anna Östlin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)


In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of N∈, where N is the input size, for any 0 ≤ ∈ < 1/9 in polynomial time unless P = NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and provide a simple, fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.
Original languageEnglish
Pages (from-to)183-197
Number of pages15
JournalJournal of Combinatorial Optimization
Issue number2-3
Publication statusPublished - 1 Dec 1999
Externally publishedYes


  • Algorithm
  • Consensus tree
  • Evolutionary tree
  • Homeomorphism
  • Time complexity

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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