Limits of local algorithms over sparse random graphs

Short summary

Local algorithms, which compute graph properties using only local information, cannot find near-maximum independent sets in sparse random d-regular graphs, refuting a prior conjecture. The best they can achieve is an independent set that is at least 1/2 + 1/(2√2) (approx. 0.853) times the size of the maximum, asymptotically as d approaches infinity.

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