Deterministic Low-Diameter Decompositions for Weighted Graphs and Distributed and Parallel Applications

Vaclav Rozhon, Michael Elkin, Christoph Grunau, Bernhard Haeupler

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

4 Scopus citations

Abstract

This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one can also efficiently compute low-diameter decompositions. This consequently implies solutions to many fundamental distance based problems using a polylogarithmic number of approximate distance computations. Our low-diameter decomposition generalizes and extends the line of work starting from [RG20] to weighted graphs in a very model-independent manner. Moreover, our clustering results have additional useful properties, including strong-diameter guarantees, separation properties, restricting cluster centers to specified terminals, and more. Applications include:-The first near-linear work and polylogarithmic depth randomized and deterministic parallel algorithm for low-stretch spanning trees (LSST) with polylogarithmic stretch. Previously, the best parallel LSST algorithm required m.no(1) work and no(1) depth and was inherently randomized. No deterministic LSST algorithm with truly sub-quadratic work and sub-linear depth was known.-The first near-linear work and polylogarithmic depth deterministic algorithm for computing an l1- into polylogarithmic dimensional space with polylogarithmic distortion. The best prior deterministic algorithms for l1-embeddings either require large polynomial work or are inherently sequential. Even when we apply our techniques to the classical problem of computing a ball-carving with strong-diameter O(log2n) in an unweighted graph, our new clustering algorithm still leads to an improvement in round complexity from O(log10n) rounds [CG21] to O( log4n).

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022
PublisherInstitute of Electrical and Electronics Engineers
Pages1114-1121
Number of pages8
ISBN (Electronic)9781665455190
DOIs
StatePublished - 28 Dec 2022
Event63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 - Denver, United States
Duration: 31 Oct 20223 Nov 2022

Conference

Conference63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022
Country/TerritoryUnited States
CityDenver
Period31/10/223/11/22

Keywords

  • Computer science
  • Computational modeling
  • Clustering algorithms
  • Distortion
  • Approximation algorithms
  • Complexity theory
  • Parallel algorithms

ASJC Scopus subject areas

  • General Computer Science

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