Congested clique algorithms for graph spanners

Merav Parter, Eylon Yogev

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

20 Scopus citations

Abstract

Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling schemes and routing to solving linear systems and spectral sparsification. A k-spanner maintains pairwise distances up to multiplicative factor of k. It is a folklore that for every n-vertex graph G, one can construct a (2k − 1) spanner with O(n 1+1/k ) edges. In a distributed setting, such spanners can be constructed in the standard CONGEST model using O(k 2 ) rounds, when randomization is allowed. In this work, we consider spanner constructions in the congested clique model, and show: a randomized construction of a (2k− 1)-spanner with O e (n 1+1/k ) edges in O(log k) rounds. The previous best algorithm runs in O(k) rounds; a deterministic construction of a (2k−1)-spanner with O e (n 1+1/k ) edges in O(log k+(log log n) 3 ) rounds. The previous best algorithm runs in O(k log n) rounds. This improvement is achieved by a new derandomization theorem for hitting sets which might be of independent interest; a deterministic construction of a O(k)-spanner with O(k · n 1+1/k ) edges in O(log k) rounds.

Original languageEnglish
Title of host publication32nd International Symposium on Distributed Computing, DISC 2018
EditorsUlrich Schmid, Josef Widder
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770927
DOIs
StatePublished - 1 Oct 2018
Externally publishedYes
Event32nd International Symposium on Distributed Computing, DISC 2018 - New Orleans, United States
Duration: 15 Oct 201819 Oct 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume121
ISSN (Print)1868-8969

Conference

Conference32nd International Symposium on Distributed Computing, DISC 2018
Country/TerritoryUnited States
CityNew Orleans
Period15/10/1819/10/18

Bibliographical note

Publisher Copyright:
© Merav Parter and Eylon Yogev.

Keywords

  • And phrases Distributed Graph Algorithms
  • Congested Clique
  • Spanner

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