The asymmetric median tree — A new model for building consensus trees
 Cynthia Phillips,
 Tandy J. Warnow
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Abstract
Inferring the consensus of a set of different evolutionary trees for a given species set is a wellstudied problem, for which several different models have been proposed. In this paper, we propose a new optimization problem for consensus tree construction, which we call the asymmetric median tree, or AMT. Our main theoretical result is the equivalence between the asymmetric median tree problem on k trees and the maximum independent set (MIS) problem on kcolored graphs. Although the problem is NPhard for three or more trees, we have polynomial time algorithms to construct the AMT for two trees and an approximation algorithm for three or more trees. We define a measure of phylogenetic resolution and show that our algorithms (both exact and approximate) produce consensus trees that on every input are at least as resolved as the standard models (strict consensus and majority tree) in use. Finally, we show that the AMT combines desirable features of many of the standard consensus tree models in use.
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 Title
 The asymmetric median tree — A new model for building consensus trees
 Book Title
 Combinatorial Pattern Matching
 Book Subtitle
 7th Annual Symposium, CPM 96 Laguna Beach, California, June 10–12, 1996 Proceedings
 Pages
 pp 234252
 Copyright
 1996
 DOI
 10.1007/3540612580_18
 Print ISBN
 9783540612582
 Online ISBN
 9783540683902
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1075
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Cynthia Phillips ^{(1)} ^{(2)}
 Tandy J. Warnow ^{(1)} ^{(2)}
 Author Affiliations

 1. Sandia National Labs, Albuquerque, NM, USA
 2. Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, USA
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