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

Authors Adi Rosén, Florent Urrutia

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Author Details

Adi Rosén
  • CNRS and Université Paris Diderot
Florent Urrutia
  • Université Paris Diderot

Funding

  • Rosén, Adi: Research supported in part by ANR project RDAM.
  • Urrutia, Florent: Research supported in part by ERC QCC and by ANR project RDAM.

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Adi Rosén and Florent Urrutia. A New Approach to Multi-Party Peer-to-Peer Communication Complexity. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 64:1-64:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ITCS.2019.64

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 Omega(kn) on the multi-party peer-to-peer randomized communication complexity of the k-player, n-bit function Disjointness, Disj_k^n. The other one is a tight lower bound of Omega(kn) on the multi-party peer-to-peer randomized communication complexity of the k-player, n-bit bitwise parity function, Par_k^n. Both lower bounds hold when n=Omega(k). The lower bound for Disj_k^n 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 Omega(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 peer-to-peer multi-party setting.
In addition to the above results for communication complexity, we also prove, using the same tools, an Omega(n) lower bound on the number of random bits necessary for the (information theoretic) private computation of the function Disj_k^n.

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Mathematics of computing → Information theory
  • Theory of computation → Cryptographic protocols
Keywords
  • communication complexity
  • multi-party communication complexity
  • peer-to-peer communication complexity
  • information complexity
  • private computation

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