Deterministic Distributed Sparse and Ultra-Sparse Spanners and Connectivity Certificates

Marcel Bezdrighin, Michael Elkin, Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, Saeed Ilchi, Václav RozhoÅ

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

Abstract

This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: • We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in polylog(n) rounds in weighted graphs. Concretely, our algorithm outputs a spanning subgraph with only n + o (n) edges in which the pairwise distances are stretched by a factor of at most O(logn · 2O(log* n)). • We provide a polylog(n)-round deterministic distributed algorithm that computes a spanner with stretch (2k - 1) and O(nk + n1+1/k log k) edges in unweighted graphs and with O(n1+1/k k) edges in weighted graphs. • We present the first polylog(n) round randomized distributed algorithm that computes a sparse connectivity certificate. For an n-node graph G, a certificate for connectivity k is a spanning subgraph H that is k-edge-connected if and only if G is k-edge-connected, and this subgraph H is called sparse if it has O(nk) edges. Our algorithm achieves a sparsity of (1 + o (1))nk edges, which is within a 2(1 + o(1)) factor of the best possible.

Original languageEnglish
Title of host publicationSPAA 2022 - Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages1-10
Number of pages10
ISBN (Electronic)9781450391467
DOIs
StatePublished - 11 Jul 2022
Event34th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2022 - Philadelphia, United States
Duration: 11 Jul 202214 Jul 2022

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference34th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2022
Country/TerritoryUnited States
CityPhiladelphia
Period11/07/2214/07/22

Keywords

  • connectivity certificates
  • distributed computing
  • low-diameter clustering
  • spanners
  • ultra-sparse spanners

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

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