A few logs suffice to build (almost) all trees: Part II

Péter L. Erdos, Michael A. Steel, László A. Székely, Tandy J. Warnow

Research output: Contribution to journalArticlepeer-review


Inferring evolutionary trees is an interesting and important problem in biology, but one that is computationally difficult as most associated optimization problems are NP-hard. Although many methods are provably statistically consistent (i.e. the probability of recovering the correct tree converges to 1 as the sequence length increases), the actual rate of convergence for different methods has not been well understood. In a recent paper we introduced a new method for reconstructing evolutionary trees called the dyadic closure method (DCM), and we showed that DCM has a very fast convergence rate. DCM runs in O(n5log n) time, where n is the number of sequences, and so, although polynomial, the computational requirements are potentially too large to be of use in practice. In this paper we present another tree reconstruction method, the witness-antiwitness method (WAM). WAM is faster than DCM, especially on random trees, and converges to the true tree topology at the same rate as DCM. We also compare WAM to other methods used to reconstruct trees, including Neighbor Joining (possibly the most popular method among molecular biologists), and new methods introduced in the computer science literature.

Original languageEnglish (US)
Pages (from-to)77-118
Number of pages42
JournalTheoretical Computer Science
Issue number1-2
StatePublished - Jun 28 1999
Externally publishedYes


  • Distance-based methods
  • Dyadic closure method
  • Evolutionary tree reconstruction
  • Phylogeny
  • Quartet methods
  • Short quartet methods
  • Witness-antiwitness method

ASJC Scopus subject areas

  • Computational Theory and Mathematics


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