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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. (1999) Approximation algorithms for the fixed-topology phylogenetic number problem. Algorithmica, Volume 25 (Number 2-3). pp. 311-329. ISSN 0178-4617.

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Official URL: http://dx.doi.org/10.1007/PL00008280

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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 for a l greater than or equal to 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 greater than or equal to 3 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: Journal Article
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Journal or Publication Title: Algorithmica
Publisher: Springer Verlag
ISSN: 0178-4617
Official Date: June 1999
Dates:
DateEvent
June 1999Published
Volume: Volume 25
Number: Number 2-3
Number of Pages: 19
Page Range: pp. 311-329
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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