如何抓住马拉松作弊者：跟踪路径的新近似算法
How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths
摘要：
给定一个无向图$G$和$G$中的顶点$s$和$t$，跟踪路径问题是寻找$G$中顶点的最小子集，其与任何$s$ - $t$路径的交集导致唯一序列。这个问题被认为是NP完全的，并且可以应用于动物迁徙跟踪和检测马拉松路线的切割，但其近似性在很大程度上是未知的。在本文中，我们解决后一个问题，给出新的算法具有近似比的$(1+ε)$，$O(\lg OPT)$和$O(\lg n)$，为$H$ -未成年人自由，一般和加权图，分别。我们还给出了$H$ -minor-free图的线性核，并对一般图的二次核进行了改进。
英文摘要：
Given an undirected graph, $G$, and vertices, $s$ and $t$ in $G$, the tracking paths problem is that of finding the smallest subset of vertices in $G$ whose intersection with any $s$-$t$ path results in a unique sequence. This problem is known to be NP-complete and has applications to animal migration tracking and detecting marathon course-cutting, but its approximability is largely unknown. In this paper, we address this latter issue, giving novel algorithms having approximation ratios of $(1+ε)$, $O(\lg OPT)$ and $O(\lg n)$, for $H$-minor-free, general, and weighted graphs, respectively. We also give a linear kernel for $H$-minor-free graphs and make improvements to the quadratic kernel for general graphs.
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。
