The asymmetric median tree — A new model for building consensus trees
 Cynthia Phillips,
 Tandy J. Warnow
 … show all 2 hide
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.
 Amir, A., and Keselman, D. Maximum agreement subtree in a set of evolutionary trees — metrics and efficient algorithms, Proceedings, FOCS '94.
 Barthelemy, J.P., McMorris, F.R. (1986) The median procedure for ntrees. Journal of Classification 3: pp. 329334
 M. Bellare and M. Sudan, “Improved nonapproximability results”, Proceedings of the TwentySixth Annual ACM Symposium on Theory of Computing, (Montreal), ACM, pp. 184–193.
 Bryant, D. (1995) Hunting for binary trees in binary character sets: efficient algorithms for extraction, enumeration, and optimization. Research Report #124. Department of Mathematics and Statistics, Canterbury University, Christchurch, New Zealand
 Day, W.H.E. (1985) Optimal algorithms for comparing trees with labelled leaves. Journal of Classification 2: pp. 728
 Day, W.H.E., Sankoff, D. (1986) Computational complexity of inferring phylogenies by compatibility. Systematic Zoology 35: pp. 224229
 Estabrook, G.F., Johnson, C.S., McMorris, F.R. (1976) A mathematical foundation for the analysis of cladistic character compatibility. Math. Biosci. 29: pp. 181187 CrossRef
 Estabrook, G.F., McMorris, F.R. (1980) When is one estimate of evolutionary relationships a refinement of another?. J. Math. Biosci. 10: pp. 327373
 M. Farach, T. Przytycka, and M. Thorup, On the agreement of many trees, Information Processing Letters, to appear.
 M. Farach and M. Thorup, Sparse Dynamic Programming for Evolutionary Tree Comparison, SIAM J. on Computing.
 Farach, M. and Thorup, M. (1994), Optimal evolutionary tree comparisons by sparse dynamic programming, Proceedings, FOCS '94.
 Garey, M.R., Johnson, D.S. (1979) Computers and Intractability: A Guide to the Theory of N PCompleteness. W.H. Freeman and Company, NY
 Gusfield, D. (1991) Efficient algorithms for inferring evolutionary trees. Networks 21: pp. 1928
 Hopcroft, J., and Karp, R.M. (1975), An O(n2.5) algorithm for maximum matching in bipartite graphs, SIAM J. on Computing, 1975, pp. 225–231.
 Johnson, D. S. (1990) A catalog of complexity classes. Algorithms and Complexity. Elsevier science publishing company, Amsterdam, pp. 67161
 Kao, Ming. Tree contractions and evolutionary trees, submitted for publication (1995).
 McMorris, F.R. and Steel, M. (1994), The complexity of the median procedure for binary trees. Proceedings of the 4th Conference of the International Federation of Classification Societies, Paris 1993, to be published in the series “Studies in Classification, Data Analysis, and Knowledge Organization” by Springer Verlag.
 Page, R. D. M. (1993) Genes, Organisms, and Areas: The Problem of Multiple Lineages. Systematic Biology 42: pp. 7784
 Page, R. D. M. (1993), Reconciled Trees and Cladistic Analysis of Historical Associations Between Genes, Organisms, and Areas, manuscript.
 Saitou, N., Nei, M. (1987) The neighborjoining method: a new method for reconstructing evolutionary trees. Mol. Biol. Evol. 4: pp. 40625
 Steel, M.A., Warnow, T.J. (1993) Kaikoura tree theorems: Computing the maximum agreement subtree. Information Processing Letters 48: pp. 7282
 Wareham, H. T. (1985) An Efficient Algorithm for Computing Ml Consensus Trees. Honors Dissertation. Department of Computer Science, Memorial University of Newfoundland, St. John's, Newfoundland
 Warnow, T.J. (1994) Tree compatibility and inferring evolutionary history. Journal of Algorithms 16: pp. 388407
 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
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 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
Continue reading...
To view the rest of this content please follow the download PDF link above.