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Approximation algorithms for the fixed-topology phylogenetic number problem

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Cryan, Mary, Goldberg, Leslie Ann and Phillips, Cynthia A. (1997) Approximation algorithms for the fixed-topology phylogenetic number problem. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)

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Abstract

In the L-phylogeny problem, one wishes to construct an evolutionary tree for a set of species represented by characters, in which each state of each character induces no more than L connected components. We consider the fixed-topology version of this problem for fixed-topologies of arbitrary degree. This version of the problem is known to be NP-complete when L is at least 3, even for degree-3 trees in which no state labels more than L+1 leaves (and therefore there is a trivial L + 1 phylogeny). We give a 2-approximation algorithm for all L for arbitrary input topologies and we give an optimal approximation algorithm that constructs a 4-phylogeny when a 3-phylogeny exists. Dynamic programming techniques, which are typically used in fixed-topology problems, cannot be applied to L-phylogeny problems. Our 2-approximation algorithm is the first application of linear programming to approximation algorithms for phylogeny problems. We extend our results to a related problem in which characters are polymorphic.

Item Type:

Report

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Computer Science

Library of Congress Subject Headings (LCSH):

Phylogeny -- Mathematical models, Trees (Graph theory)

Series Name:

Department of Computer Science research report

Publisher:

University of Warwick. Department of Computer Science

Official Date:

June 1997

Dates:

Date	Event
June 1997	Completion

Number:

Number 327

Number of Pages:

DOI:

CS-RR-327

Institution:

University of Warwick

Theses Department:

Department of Computer Science

Status:

Not Peer Reviewed

Publication Status:

Unpublished

Publisher Statement:

M. Cryan, L.A. Goldberg and C.A. Phillips, “Approximation Algorithms for the Fixed-Topology Phylogenetic Number Problem”, <i>Proceedings of Combinatorial Pattern Matching</i> <b>8</b>, (1997)

Funder:

European Strategic Programme of Research and Development in Information Technology (ESPRIT), University of Warwick, United States. Department of Energy

Grant number:

20244 (ESPRIT), 0951CSA (UoW), DE-AC04-76AL85000 (DOE)

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