Using Semi-definite Programming to Enhance Supertree Resolvability
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Supertree methods are used to construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Since accurate reconstruction methods are currently limited to a maximum of few dozens of taxa, the use of a supertree method in order to construct the tree of life is inevitable.
Supertree methods are broadly divided according to the input trees: When the input trees are unrooted, the basic reconstruction unit is a quartet tree. In this case, the basic decision problem of whether there exists a tree that agrees with all quartets is NP-complete. On the other hand, when the input trees are rooted, the basic reconstruction unit is a rooted triplet, and the above decision problem has a polynomial time algorithm. However, when there is no tree which agrees with all triplets, it would be desirable to find the tree that agrees with the maximum number of triplets. However, this optimization problem was shown to be NP-hard. Current heuristic approaches perform mincut on a graph representing the triplets inconsistency and return a tree that is guaranteed to satisfy some required properties.
In this work we present a different heuristic approach that guarantees the properties provided by the current methods and give experimental evidence that it significantly outperforms currently used methods. This method is based on divide and conquer where we use a semi-definite programming approach in the divide step.
KeywordsConnectivity Graph Internal Vertex Input Tree Good Edge Parsimony Score
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- [ARV04]Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. In: Symposium on the Foundations of Computer Science (2004)Google Scholar
- [CT05]Chor, B., Tuller, T.: Maximum likelihood of evolutionary trees is hard. In: RECOMB (2005)Google Scholar
- [FM82]Fiduccia, C.M., Mattheyses, R.M.: A linear time heuristic for improving network partitions. In: Design Automation Conference, pp. 175–181 (1982)Google Scholar
- [HKW96]Henzinger, M.R., King, V., Warnow, T.: Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. In: SODA, pp. 333–340 (1996)Google Scholar
- [KL70]Kernighan, B.W., Lin, S.: An ecient heuristic procedure for partitioning graphs. The Bell System Technical Journal 29(2), 291–307 (1970)Google Scholar
- [MS04]Moran, S., Snir, S.: Convex recoloring of strings and trees: Definitions, hardness results and algorithms. submitted (2004)Google Scholar
- [PSDW]Piel, W., Sanderson, M., Donoghue, M., Walsh, M.: Treebase, http://www.treebase.org
- [SN87]Saitou, N., Nei, M.: The neighbor-joining method: A new method for reconstructing phylogenetic trees. Molecular Biology and Evolution 4 (1987)Google Scholar