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arXiv · 2504.01091

Local Constant Approximation for Dominating Set on Graphs Excluding Large Minors

Marthe Bonamy·Cyril Gavoille·Timothé Picavet·Alexandra Wesolek
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Abstract

We show that graphs excluding $K_{2,t}$ as a minor admit a $f(t)$-round $50$-approximation deterministic distributed algorithm for Minimum Dominating Set. The result extends to Minimum Vertex Cover. Though fast and approximate distributed algorithms for such problems were already known for $H$-minor-free graphs, all of them have an approximation ratio depending on the size of $H$. To the best of our knowledge, this is the first example of a large non-trivial excluded minor leading to fast and constant-approximation distributed algorithms, where the ratio is independent of the size of $H$. A new key ingredient in the analysis of these distributed algorithms is the use of asymptotic dimension.

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Marthe Bonamy, Cyril Gavoille, Timothé Picavet, Alexandra Wesolek. 2025-04-01. Local Constant Approximation for Dominating Set on Graphs Excluding Large Minors. https://arxiv.org/abs/2504.01091

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