research-article

On the power of the congested clique model

Authors:

Andrew Drucker,

Rotem OshmanAuthors Info & Claims

PODC '14: Proceedings of the 2014 ACM symposium on Principles of distributed computing

Pages 367 - 376

https://doi.org/10.1145/2611462.2611493

Published: 15 July 2014 Publication History

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 well-known 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 subgraphs. 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.

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Index Terms

On the power of the congested clique model
1. Theory of computation
  1. Design and analysis of algorithms
  2. Models of computation

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cover image ACM Conferences

PODC '14: Proceedings of the 2014 ACM symposium on Principles of distributed computing

July 2014

444 pages

ISBN:9781450329446

DOI:10.1145/2611462

General Chair:
Magnús Halldórsson
Reykjavik Universite, Iceland
,
Program Chair:
Shlomi Dolev
Ben-Gurion University, Israel

Copyright © 2014 ACM.

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Published: 15 July 2014

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