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arXiv · 2104.12337

How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths

Michael T. Goodrich·Siddharth Gupta·Hadi Khodabandeh·Pedro Matias
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Abstract

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 $(1+\epsilon)$, $O(\lg OPT)$ 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.

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Michael T. Goodrich, Siddharth Gupta, Hadi Khodabandeh, Pedro Matias. 2021-04-26. How to Catch Marathon Cheaters: New Approximation Algorithms for Tracking Paths. https://arxiv.org/abs/2104.12337

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