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arXiv · 1402.2549

Local Approximability of Minimum Dominating Set on Planar Graphs

Miikka Hilke·Christoph Lenzen·Jukka Suomela
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Abstract

We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a $(7-\epsilon)$-approximation of a minimum dominating set on planar graphs, for any positive constant $\epsilon$. In prior work, the best lower bound on the approximation ratio has been $5-\epsilon$; there is also an upper bound of $52$.

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Miikka Hilke, Christoph Lenzen, Jukka Suomela. 2014-02-11. Local Approximability of Minimum Dominating Set on Planar Graphs. https://arxiv.org/abs/1402.2549

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