树空间中测地距离的快速算法
A Fast Algorithm for Computing Geodesic Distances in Tree Space
摘要：
比较和计算系统发育树之间的距离是重要的生物学问题，特别是对于边长起重要作用的模型。两棵具有边长的系统发育树之间的测地线距离度量是Billera、Holmes和Vogtmann引入的连续树空间中它们之间的最短路径的长度。这棵树空间提供了一个强大的工具，用于研究和比较系统发育树，无论是在表现出一个自然的距离措施，并在提供一个类似于欧几里德的结构，解决优化问题的树。一个重要的公开问题是找到一个多项式时间算法来寻找测地线在树空间。本文给出了这样一个算法，它从一个简单的初始路径开始，经过一系列连续的较短路径，直到获得测地线。
英文摘要：
Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and Vogtmann. This tree space provides a powerful tool for studying and comparing phylogenetic trees, both in exhibiting a natural distance measure and in providing a Euclidean-like structure for solving optimization problems on trees. An important open problem is to find a polynomial time algorithm for finding geodesics in tree space. This paper gives such an algorithm, which starts with a simple initial path and moves through a series of successively shorter paths until the geodesic is attained.
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