Approximation algorithms for the fixed-topology phylogenetic number problem
UNSPECIFIED. (1999) Approximation algorithms for the fixed-topology phylogenetic number problem. ALGORITHMICA, 25 (2-3). pp. 311-329. ISSN 0178-4617Full text not available from this repository.
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|
|Number of Pages:||19|
|Page Range:||pp. 311-329|
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