系统发生网络类别的近似度量
Proximity Measures for Classes of Phylogenetic Networks
AI总结：
研究系统发生网络类别，考虑基于叶添加、有效弧删除和弧删除的三种近似度量，研究其成对可比性、复杂性结果及网络类别的极值界限，以衡量给定网络与特定类别接近程度。
AI中文摘要：
系统发生网络用于表示物种的进化历史。由于生物学解释和计算优势，研究人员专注于受限的系统发生网络类别，如树子、果园和基于树的网络。这些类别捕捉了不同的树状概念。一个自然问题是给定网络与特定类别有多接近，这促使对近似度量进行研究。本文考虑基于叶添加、有效弧删除和弧删除的三种近似度量，研究它们的成对可比性，证明复杂性结果，并推导树、树子、果园和基于树的网络类别的极值界限。
英文摘要：
Phylogenetic networks are used to represent the evolutionary history of species. Due to biological interpretations and computational advantages, researchers have focused on restricted classes of phylogenetic networks, such as tree-child, orchard, and tree-based. These classes capture different notions of tree-likeness: tree-child networks require every internal vertex to have a taxon reachable by a tree path, orchard networks are trees with horizontal arcs (for modelling histories rife with horizontal gene transfers), and tree-based networks are trees with additional (not-necessarily horizontal) arcs. A natural question to ask is ``how far is a given network from belonging to a particular class?'' This motivates the study of proximity measures, which measure the minimum number of graph modifications required to transform a network into one belonging to a particular class. In this paper, we consider three proximity measures based on leaf addition, valid arc deletion, and arc deletion. We study pairwise comparability of the proximity measures, prove complexity results, and derive extremal bounds for the classes of tree, tree-child, orchard, and tree-based networks.
