Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks release_wec72oufznevtdrbpzevg7ldxi

by Jaroslaw Byrka, Pawel Gawrychowski, Katharina T. Huber, Steven Kelk

Released as a article .

2007  

Abstract

This article concerns the following question arising in computational evolutionary biology. For a given subclass of phylogenetic networks, what is the maximum value of 0 <= p <= 1 such that for every input set T of rooted triplets, there exists some network N(T) from the subclass such that at least p|T| of the triplets are consistent with N(T)? Here we prove that the set containing all triplets (the full triplet set) in some sense defines p, and moreover that any network N achieving fraction p' for the full triplet set can be converted in polynomial time into an isomorphic network N'(T) achieving >= p' for an arbitrary triplet set T. We demonstrate the power of this result for the field of phylogenetics by giving worst-case optimal algorithms for level-1 phylogenetic networks (a much-studied extension of phylogenetic trees), improving considerably upon the 5/12 fraction obtained recently by Jansson, Nguyen and Sung. For level-2 phylogenetic networks we show that p >= 0.61. We note that all the results in this article also apply to weighted triplet sets.
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Type  article
Stage   submitted
Date   2007-11-15
Version   v2
Language   en ?
arXiv  0710.3258v2
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