1. Optimal Communication Rates and Combinatorial Properties for Common Randomness Generation.
- Author
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Han, Yanjun, Tatwawadi, Kedar, Kurri, Gowtham R., Zhou, Zhengqing, Prabhakaran, Vinod M., and Weissman, Tsachy
- Subjects
COMMONS ,LINEAR programming ,HYPERGRAPHS ,DISTRIBUTED algorithms - Abstract
We study common randomness generation problems where $n$ players aim to generate same sequences of random coin flips where some subsets of the players share an independent common coin which can be tossed multiple times, and there is a publicly seen blackboard through which the players communicate with each other. We provide a tight representation of the optimal communication rates via linear programming, and more importantly, propose explicit algorithms for the optimal distributed simulation for a wide class of hypergraphs. In particular, the optimal communication rate in complete hypergraphs is still achievable in sparser hypergraphs containing a path-connected cycle-free cluster of topologically connected components. Some key steps in analyzing the upper bounds rely on two different definitions of connectivity in hypergraphs, which may be of independent interest. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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