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arXiv · 2203.03229

Distributed distance domination in graphs with no $K_{2,t}$-minor

Andrzej Czygrinow·Michał Hanćkowiak·Marcin Witkowski
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Abstract

We prove that a simple distributed algorithm finds a constant approximation of an optimal distance-$k$ dominating set in graphs with no $K_{2,t}$-minor. The algorithm runs in a constant number of rounds. We further show how this procedure can be used to give a distributed algorithm which given $\epsilon>0$ and $k,t\in \mathbb{Z}^+$ finds in a graph $G=(V,E)$ with no $K_{2,t}$-minor a distance-$k$ dominating set of size at most $(1+\epsilon)$ of the optimum. The algorithm runs in $O(\log^*{|V|})$ rounds in the Local model. In particular, both algorithms work in outerplanar graphs.

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Andrzej Czygrinow, Michał Hanćkowiak, Marcin Witkowski. 2022-03-07. Distributed distance domination in graphs with no $K_{2,t}$-minor. https://arxiv.org/abs/2203.03229

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