Beeping Shortest Paths via Hypergraph Bipartite Decomposition

Fabien Dufoulon, Yuval Emek, Ran Gelles

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

Abstract

Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in O(D log log n + log3 n) rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in O(D log2 n + log3 n) rounds with high probability. Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the hyperedge set of a hypergraph H = (VH, EH) into k = Θ(log2 n) disjoint subsets F1 ∪ · · · ∪ Fk = EH such that the (sub-)hypergraph (VH, Fi) is bipartite in the sense that there exists a vertex subset U ⊆ V such that |U ∩ e| = 1 for every e ∈ Fi. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.

Original languageEnglish
Title of host publication14th Innovations in Theoretical Computer Science Conference, ITCS 2023
EditorsYael Tauman Kalai
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772631
DOIs
StatePublished - 1 Jan 2023
Event14th Innovations in Theoretical Computer Science Conference, ITCS 2023 - Cambridge, United States
Duration: 10 Jan 202313 Jan 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume251
ISSN (Print)1868-8969

Conference

Conference14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Country/TerritoryUnited States
CityCambridge
Period10/01/2313/01/23

Bibliographical note

Publisher Copyright:
© Fabien Dufoulon, Yuval Emek, and Ran Gelles; licensed under Creative Commons License CC-BY 4.0.

Keywords

  • Beeping Networks
  • Hypergraph Bipartite Decomposition
  • Shortest Paths

Fingerprint

Dive into the research topics of 'Beeping Shortest Paths via Hypergraph Bipartite Decomposition'. Together they form a unique fingerprint.

Cite this