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arXiv · 2207.08678

A quadratic-order problem kernel for the traveling salesman problem parameterized by the vertex cover number

René van Bevern·Daniel A. Skachkov
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Abstract

The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with $τ^2+τ$ vertices for GTSP, where $τ$ is the vertex cover number of the input graph. Any $α$-approximate solution for the problem kernel also gives an $α$-approximate solution for the original instance, for any $α\geq1$.

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BibTeXRIS

René van Bevern, Daniel A. Skachkov. 2023-10-11. A quadratic-order problem kernel for the traveling salesman problem parameterized by the vertex cover number. https://arxiv.org/abs/2207.08678

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