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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
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 |
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| 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: |
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| 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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