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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 simultaneous number-in-hand multi-party communication protocols, we have k players, who each receive a private input, and wish to compute a joint function of their inputs. The players simultaneously each send a single message to a referee, who then outputs the value of the function. The cost of the protocol is the total number of bits sent to the(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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