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- W4287029123 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." @default.
- W4287029123 created "2022-07-25" @default.
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- W4287029123 date "2021-08-03" @default.
- W4287029123 modified "2023-09-23" @default.
- W4287029123 title "Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set" @default.
- W4287029123 doi "https://doi.org/10.48550/arxiv.2108.01430" @default.
- W4287029123 hasPublicationYear "2021" @default.
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