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We show that any randomised Monte Carlo distributed algorithm for the Lovász local lemma requires Omega(log log n) communication rounds, assuming that it finds a correct assignment with high probability. Our result holds even in the special case of d = O(1), where d is the maximum degree of the dependency graph. By prior work, there are distributed(More)
In the subgraph-freeness problem, we are given a constant-size graph H, and wish to determine whether the network contains H as a subgraph or not. The property-testing relaxation of the problem only requires us to distinguish graphs that are H-free from graphs that are -far from H-free, in the sense that an -fraction of their edges must be removed to obtain(More)
In this paper we initiate the study of property testing in simultaneous and non-simultaneous multi-party communication complexity, focusing on testing triangle-freeness in graphs. We consider the coordinator model, where we have k players receiving private inputs, and a coordinator who receives no input; the coordinator can communicate with all the players,(More)
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