Constant-Round Near-Optimal Spanners in Congested Clique

Shiri Chechik, Tianyi Zhang

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

Abstract

Graph spanners have been extensively studied in the literature of graph algorithms. In an undirected weighted graph G = (V, E,ω) on n vertices, a t-spanner of G is a subgraph that preserves pairwise distances up to a multiplicative stretch factor of t . It is well-known that, for any integer k, a (2k - 1)-spanner with O(n1+1/k ) edges always exists, and the stretch-sparsity balance is tight under the girth conjecture by Erdos. In this paper, we are interested in efficient algorithms for spanners in the distributed setting. Specifically, we present constant-round congested clique algorithms for spanners with nearly optimal stretch-sparsity trade-offs: (2k-1)-spanners with O(n1+1/k ) edges in unweighted graphs (i.e. ω 1). (1 + ) (2k - 1)-spanners with O(n1+1/k ) edges in weighted graphs. (2k-1)-spanners withO(kn1+1/k ) edges in weighted graphs.

Original languageEnglish
Title of host publicationPODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages325-334
Number of pages10
ISBN (Electronic)9781450392624
DOIs
StatePublished - 20 Jul 2022
Event41st ACM Symposium on Principles of Distributed Computing, PODC 2022 - Salerno, Italy
Duration: 25 Jul 202229 Jul 2022

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference41st ACM Symposium on Principles of Distributed Computing, PODC 2022
Country/TerritoryItaly
CitySalerno
Period25/07/2229/07/22

Keywords

  • congested clique
  • shortest paths
  • spanners

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