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arXiv · 2108.01430

Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set

Václav Blažej·Pratibha Choudhary·Dušan Knop·Jan Matyáš Křišťan·Ondřej Suchý·Tomáš Valla
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Abstract

Consider a vertex-weighted graph $G$ with a source $s$ and a target $t$. Tracking Paths requires finding a minimum weight set of vertices (trackers) such that the sequence of trackers in each path from $s$ to $t$ is unique. In this work, we derive a factor $6$-approximation algorithm for Tracking Paths in weighted graphs and a factor $4$-approximation algorithm if the input is unweighted. This is the first constant factor approximation for this problem. While doing so, we also study approximation of the closely related $r$-Fault Tolerant Feedback Vertex Set problem. There, for a fixed integer $r$ and a given vertex-weighted graph $G$, the task is to find a minimum weight set of vertices intersecting every cycle of $G$ in at least $r+1$ vertices. We give a factor $\mathcal{O}(r)$ approximation algorithm for $r$-Fault Tolerant Feedback Vertex Set if $r$ is a constant.

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Václav Blažej, Pratibha Choudhary, Dušan Knop, Jan Matyáš Křišťan, Ondřej Suchý, Tomáš Valla. 2021-08-03. Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set. https://arxiv.org/abs/2108.01430

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