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Local algorithms for independent sets are half-optimal

Rahman, Mustazee and Virág, Bálint (2017) 'Local algorithms for independent sets are half-optimal.', Annals of probability., 45 (3). pp. 1543-1577.


We show that the largest density of factor of i.i.d. independent sets in the d -regular tree is asymptotically at most ( log d ) / d as d → ∞ . This matches the lower bound given by previous constructions. It follows that the largest independent sets given by local algorithms on random d -regular graphs have the same asymptotic density. In contrast, the density of the largest independent sets in these graphs is asymptotically 2 ( log d ) / d . We prove analogous results for Poisson–Galton–Watson trees, which yield bounds for local algorithms on sparse Erdős–Rényi graphs.

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Publisher statement:Copyright © 2017 Institute of Mathematical Statistics
Date accepted:11 January 2016
Date deposited:04 October 2021
Date of first online publication:15 May 2017
Date first made open access:04 October 2021

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