系统发育网络中最大化三元组一致性的最坏情况最优近似算法
Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks
摘要：
这篇文章关注计算进化生物学中出现的以下问题。对于一个给定的系统发育网络子类，0 <= p <= 1的最大值是多少，使得对于每个有根三元组的输入集T，存在来自该子类的某个网络N（T），使得至少p个三元组的|T|与N（T）一致？在这里，我们证明了包含所有三元组的集合（完整三元组集合）在某种意义上定义了p，而且对于完整三元组集合，任何达到分数p'的网络N都可以在多项式时间内转换为对于任意三元组集合T，达到>= p'的同构网络N '（T）。我们证明了这一结果的权力，为遗传学领域的最坏情况下的最优算法的水平-1系统发育网络（系统发育树的一个深入研究的扩展），大大提高了5/12分数最近获得的扬松，阮和宋。对于2级系统发育网络，我们表明p >= 0.61。我们注意到，本文中的所有结果也适用于加权三元组集。
英文摘要：
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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