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

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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
Journal or Publication Title:	ALGORITHMICA
Publisher:	SPRINGER-VERLAG
ISSN:	0178-4617
Date:	October 1999
Volume:	25
Number:	2-3
Number of Pages:	19
Page Range:	pp. 311-329
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/12738

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