Optimal Communication Rates for Zero-Error Distributed Simulation under Blackboard Communication Protocols
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We study the distributed simulation problem where n users aim to generate same sequences of random coin flips. Some subsets of the users share an independent common coin which can be tossed multiple times, and there is a publicly seen blackboard through which the users communicate with each other. We show that when each coin is shared among subsets of size k, the communication rate (i.e., number of bits on blackboard per bit in generated sequence) is at least n-k/n-1. Moreover, if the size-k subsets with common coins contain a path-connected cluster of topologically connected components, we propose a communication scheme which achieves the optimal rate n-k/n-1. Some key steps in analyzing the upper bounds rely on two different definitions of connectivity in hypergraphs, which may be of independent interest.
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