The communication complexity of multiparty set disjointness under product distributions

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In the multiparty number-in-hand set disjointness problem, we have k players, with private inputs X1,...,Xk ? [n]. The players' goal is to check whether ?=1k X? = .... It is known that in the shared blackboard model of communication, set disjointness requires ?(n logk + k) bits of communication, and in the coordinator model, it requires ?(kn) bits. However, these two lower bounds require that the players' inputs can be highly correlated. We study the communication complexity of multiparty set disjointness under product distributions, and ask whether the problem becomes significantly easier, as it is known to become in the two-party case. Our main result is a nearly-tight bound of (n1-1/k + k) for both the shared blackboard model and the coordinator model. This shows that in the shared blackboard model, as the number of players grows, having independent inputs helps less and less; but in the coordinator model, when k is very large, having independent inputs makes the problem much easier. Both our upper and our lower bounds use new ideas, as the original techniques developed for the two-party case do not scale to more than two players.

Original languageEnglish
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
PublisherAssociation for Computing Machinery
Pages1194-1207
Number of pages14
ISBN (Electronic)9781450380539
DOIs
StatePublished - 15 Jun 2021
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: 21 Jun 202125 Jun 2021

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period21/06/2125/06/21

Keywords

  • communication complexity
  • product distributions
  • set disjointness

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