On the power of the congested clique model

Andrew Drucker, Fabian Kuhn, Rotem Oshman

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

Abstract

We study the computation power of the congested clique, a model of distributed computation where n players communicate with each other over a complete network in order to compute some function of their inputs. The number of bits that can be sent on any edge in a round is bounded by a parameter b. We consider two versions of the model: in the first, the players communicate by unicast, allowing them to send a different message on each of their links in one round; in the second, the players communicate by broadcast, sending one message to all their neighbors. It is known that the unicast version of the model is quite powerful; to date, no lower bounds for this model are known. In this paper we provide a partial explanation by showing that the unicast congested clique can simulate powerful classes of bounded-depth circuits, implying that even slightly super-constant lower bounds for the congested clique would give new lower bounds in circuit complexity. Moreover, under a widely-believed conjecture on matrix multiplication, the triangle detection problem, studied in [8], can be solved in O(nε) time for any ε > 0. The broadcast version of the congested clique is the wellknown multi-party shared-blackboard model of communication complexity (with number-in-hand input). This version is more amenable to lower bounds, and in this paper we show that the subgraph detection problem studied in [8] requires polynomially many rounds for several classes of sub-graphs. We also give upper bounds for the subgraph detection problem, and relate the hardness of triangle detection in the broadcast congested clique to the communication complexity of set disjointness in the 3-party number-on-forehead model.

Original languageEnglish
Title of host publicationPODC 2014 - Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages367-376
Number of pages10
ISBN (Print)9781450329446
DOIs
StatePublished - 2014
Externally publishedYes
Event2014 ACM Symposium on Principles of Distributed Computing, PODC 2014 - Paris, France
Duration: 15 Jul 201418 Jul 2014

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference2014 ACM Symposium on Principles of Distributed Computing, PODC 2014
Country/TerritoryFrance
CityParis
Period15/07/1418/07/14

Keywords

  • Congested clique
  • Lower bounds
  • Subgraph detection

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