在理论和实践中检验系统发育决定性
Checking Phylogenetic Decisiveness in Theory and in Practice
摘要：
假设我们有一个由$n$分类群组成的集合$X$，并且我们从$k$基因座获得信息，从这些信息构建$X$的同源群。每个位点仅提供一小部分分类群的信息。问题是这些数据是否足以构建一个可靠的遗传学。决策性问题组合地表达了这个问题。尽管人们已经知道了决策的精确特征，但问题的复杂性仍然是个未知数。在这里，我们将决策性与超图着色问题联系起来。我们使用这个想法来（1）获得实现决策性所需的覆盖量的下限，（2）设计决策性的精确算法，（3）开发问题简化规则，并使用它们来获得具有少量位点的输入的有效算法，以及（4）设计决策性问题的整数线性规划公式，这使我们能够分析实践中出现的数据集。
英文摘要：
Suppose we have a set $X$ consisting of $n$ taxa and we are given information from $k$ loci from which to construct a phylogeny for $X$. Each locus offers information for only a fraction of the taxa. The question is whether this data suffices to construct a reliable phylogeny. The decisiveness problem expresses this question combinatorially. Although a precise characterization of decisiveness is known, the complexity of the problem is open. Here we relate decisiveness to a hypergraph coloring problem. We use this idea to (1) obtain lower bounds on the amount of coverage needed to achieve decisiveness, (2) devise an exact algorithm for decisiveness, (3) develop problem reduction rules, and use them to obtain efficient algorithms for inputs with few loci, and (4) devise an integer linear programming formulation of the decisiveness problem, which allows us to analyze data sets that arise in practice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
