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arXiv · 2008.09806

Structural Parameterizations of Tracking Paths Problem

Pratibha Choudhary·Venkatesh Raman
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Abstract

Given a graph $G$ with source and destination vertices $s,t\in V(G)$ respectively, \textsc{Tracking Paths} asks for a minimum set of vertices $T\subseteq V(G)$, such that the sequence of vertices encountered in each simple path from $s$ to $t$ is unique. The problem was proven \textsc{NP}-hard \cite{tr-j} and was found to admit a quadratic kernel when parameterized by the size of the desired solution \cite{quadratic}. Following recent trends, for the first time, we study \textsc{Tracking Paths} with respect to structural parameters of the input graph, parameters that measure how far the input graph is, from an easy instance. We prove that \textsc{Tracking Paths} admits fixed-parameter tractable (\textsc{FPT}) algorithms when parameterized by the size of vertex cover, and the size of cluster vertex deletion set for the input graph.

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Pratibha Choudhary, Venkatesh Raman. 2020-08-22. Structural Parameterizations of Tracking Paths Problem. https://arxiv.org/abs/2008.09806

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