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arXiv · 2108.02697

A tight local algorithm for the minimum dominating set problem in outerplanar graphs

Marthe Bonamy·Linda Cook·Carla Groenland·Alexandra Wesolek
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Abstract

We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a $(5-\varepsilon)$-approximation, for any $\varepsilon>0$. Our algorithm only requires knowledge of the degree of a vertex and of its neighbors, so that large messages and unique identifiers are not needed.

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Marthe Bonamy, Linda Cook, Carla Groenland, Alexandra Wesolek. 2021-08-05. A tight local algorithm for the minimum dominating set problem in outerplanar graphs. https://arxiv.org/abs/2108.02697

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