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Tree reconstruction from partial orders

  • Sampath Kannan
  • Tandy Warnow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 709)

Abstract

The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Sampath Kannan
    • 1
  • Tandy Warnow
    • 2
  1. 1.University of ArizonaTucson
  2. 2.Sandia National LaboratoriesAlbuquerque

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