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Random Centres and the $\varepsilon$-Dependence of Constant-Round Planar Domination
It was recently shown (arXiv:2610.09618) that the infimum of the approximation ratios of deterministic constant-round LOCAL algorithms for minimum dominating set on planar graphs is 7. The $(7+\varepsilon)$-approximation given there runs in $T_0+O((c_0/\varepsilon)^κ)$ rounds with $κ=\ln 3/\ln(24/23
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