Sparsifying congested cliques and core-periphery networks

Alkida Balliu, Pierre Fraigniaud, Zvi Lotker, Dennis Olivetti

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

1 Scopus citations

Abstract

The core-periphery network architecture proposed by Avin et al. [ICALP 2014] was shown to support fast computation for many distributed algorithms, while being much sparser than the congested clique. For being efficient, the core-periphery architecture is however bounded to satisfy three axioms, among which is the capability of the core to emulate the clique, i.e., to implement the all-to-all communication pattern, in O(1) rounds in the CONGEST model. In this paper, we show that implementing all-to-all communication in k rounds can be done in n-node networks with roughly n2/k edges, and this bound is tight. Hence, sparsifying the core beyond just saving a fraction of the edges requires to relax the constraint on the time to simulate the congested clique. We show that, for p ≫ √log n/n, a random graph in Gn,p can, w.h.p., perform the all-to-all communication pattern in O(min{ 1/p2, np}) rounds. Finally, we show that if the core can emulate the congested clique in t rounds, then there exists a distributed MST construction algorithm performing in O(t log n) rounds. Hence, for t = O(1), our (deterministic) algorithm improves the best known (randomized) algorithm for constructing MST in core-periphery networks by a factor Θ(log n).

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 23rd International Colloquium, SIROCCO 2016, Revised Selected Papers
EditorsJukka Suomela
PublisherSpringer Verlag
Pages307-322
Number of pages16
ISBN (Print)9783319483139
DOIs
StatePublished - 1 Jan 2016
Event23rd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2016 - Helsinki, Finland
Duration: 19 Jul 201621 Jul 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9988 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2016
Country/TerritoryFinland
CityHelsinki
Period19/07/1621/07/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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