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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 (Unpublished)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 | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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| Number: | Number 327 | ||||
| Number of Pages: | 17 | ||||
| DOI: | CS-RR-327 | ||||
| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
| Reuse Statement (publisher, data, author rights): | 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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