发表机构
Department of Applied Mathematics, Faculty of Science and Engineering, Waseda University（早稻田大学理工学术院应用数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对系统发育网络的最小层问题，提出两种整数线性规划方法，分别用于求解层至多为1的子图的精确解和一般情况的启发式解，实验验证了方法的实用性，且最小层可作为网络拓扑复杂性的替代度量。
AI 中文摘要
系统发育网络对涉及网状事件的进化历史进行建模，但其结构复杂性导致难以解读。提取其简单子结构既可以阐明进化路径，也能源化网络自身的复杂性。对于给定的有根近二元系统发育网络，最小层问题要求找到一个生成子图，该子图具有相同的根和叶集，且其层最小，即尽可能接近树。最小层为零的网络被称为基于树的网络，可在线性时间内识别。然而，最小层问题在一般情况下是NP难的。现有最先进的算法依赖于对解空间的穷举搜索，因此仅适用于规模有限的网络。本文中，我们针对最小层问题提出两种基于整数线性规划的方法：一种用于寻找层最多为1的此类子图的精确模型，另一种用于一般情况的启发式模型。计算实验证实了这两种模型的实用性。将其应用于祖先重组图表明，最小层可作为推断网络拓扑复杂性的替代度量。
英文摘要
Phylogenetic networks model evolutionary histories that involve reticulate events, but their structural complexity makes them difficult to interpret. Extracting their simple substructures both clarifies the evolutionary pathways and quantifies the complexity of the networks themselves. For a given rooted almost-binary phylogenetic network, the Level Minimization problem asks for a spanning subgraph that has the same root and leaf-set and whose level is minimum, i.e., which is as close to a tree as possible. Networks for which the minimum level is zero are known as tree-based networks and can be recognized in linear time. However, Level Minimization is NP-hard in general. State-of-the-art algorithms rely on exhaustive searches of the solution spaces and hence apply only to networks of limited size. In this paper, we propose two methods for Level Minimization using integer linear programming: an exact formulation for finding such a subgraph of level at most one, and a heuristic formulation for the general case. Computational experiments confirmed the practicality of both formulations. An application to ancestral recombination graphs suggests that the minimum level provides an alternative measure of the topological complexity of an inferred network.
Comments12 pages, 6 figures
