Large independent sets on random d-regular graphs with d small
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In this paper, we present a prioritized local algorithm that computes a maximal independent set on a random d-regular graph with small and fixed connectivity d. Combining different strategies, we compute new lower bounds on the independence ratio ∀ d ∈ [5,100], d∈N. All the new bounds improve upon the best previous bounds. Moreover, for independent set in random 3-regular graph, we experimentally extrapolate, by finite-size analysis, the asymptotic value of the independence ratio at α_LB=0.445327.
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