A Unified Framework for Hopsets

Ofer Neiman, Idan Shabat

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

Abstract

Given an undirected graph G = (V,E), an (α, β)-hopset is a graph H = (V,E'), so that adding its edges to G guarantees every pair has an α-approximate shortest path that has at most β edges (hops), that is, dG(u, v) ≤ d (β) G∪H(u, v) ≤ α dG(u, v). Given the usefulness of hopsets for fundamental algorithmic tasks, several different algorithms and techniques were developed for their construction, for various regimes of the stretch parameter α. In this work we devise a single algorithm that can attain all state-of-the-art hopsets for general graphs, by choosing the appropriate input parameters. In fact, in some cases it also improves upon the previous best results. We also show a lower bound on our algorithm. In [3], given a parameter k, a (O(kϵ),O(k1-ϵ))-hopset of size O(n1+1/k) was shown for any n-vertex graph and parameter 0 < ϵ < 1, and they asked whether this result is best possible. We resolve this open problem, showing that any (α, β)-hopset of size O(n1+1/k) must have α β ≥ Ω(k).

Original languageAmerican English
Title of host publication30th Annual European Symposium on Algorithms, ESA 2022
EditorsShiri Chechik, Gonzalo Navarro, Eva Rotenberg, Grzegorz Herman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772471
DOIs
StatePublished - 1 Sep 2022
Event30th Annual European Symposium on Algorithms, ESA 2022 - Berlin/Potsdam, Germany
Duration: 5 Sep 20229 Sep 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume244

Conference

Conference30th Annual European Symposium on Algorithms, ESA 2022
Country/TerritoryGermany
CityBerlin/Potsdam
Period5/09/229/09/22

Keywords

  • Graph Algorithms
  • Hopsets
  • Shortest Paths

All Science Journal Classification (ASJC) codes

  • Software

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