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arXiv · 1901.01178

A New Approach to Multi-Party Peer-to-Peer Communication Complexity

Adi Rosén·Florent Urrutia
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Abstract

We introduce new models and new information theoretic measures for the study of communication complexity in the natural peer-to-peer, multi-party, number-in-hand setting. We prove a number of properties of our new models and measures, and then, in order to exemplify their effectiveness, we use them to prove two lower bounds. The more elaborate one is a tight lower bound of $Ω(kn)$ on the multi-party peer-to-peer randomized communication complexity of the $k$-player, $n$-bit Disjointness function. The other one is a tight lower bound of $Ω(kn)$ on the multi-party peer-to-peer randomized communication complexity of the $k$-player, $n$-bit bitwise parity function. Both lower bounds hold when ${n=Ω(k)}$. The lower bound for Disjointness improves over the lower bound that can be inferred from the result of Braverman et al.~(FOCS 2013), which was proved in the coordinator model and can yield a lower bound of $Ω(kn/\log k)$ in the peer-to-peer model. To the best of our knowledge, our lower bounds are the first tight (non-trivial)lower bounds on communication complexity in the natural {\em peer-to-peer} multi-party setting. In addition to the above results for communication complexity, we also prove, using the same tools, an $Ω(n)$ lower bound on the number of random bits necessary for the (information theoretic) private computation of the $k$-player, $n$-bit Disjointness function .

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Adi Rosén, Florent Urrutia. 2020-09-30. A New Approach to Multi-Party Peer-to-Peer Communication Complexity. https://arxiv.org/abs/1901.01178

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