Reachability and shortest paths in the broadcast congest model

Shiri Chechik, Doron Mukhtar

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

7 Scopus citations

Abstract

In this paper we study the time complexity of the single-source reachability problem and the single-source shortest path problem for directed unweighted graphs in the Broadcast CONGEST model. We focus on the case where the diameter D of the underlying network is constant. We show that for the case where D = 1 there is, quite surprisingly, a very simple algorithm that solves the reachability problem in 1(!) round. In contrast, for networks with D = 2, we show that any distributed algorithm (possibly randomized) for this problem requires Ω(pn/ log n ) rounds. Our results therefore completely resolve (up to a small polylog factor) the complexity of the single-source reachability problem for a wide range of diameters. Furthermore, we show that when D = 1, it is even possible to get an almost 3 – approximation for the all-pairs shortest path problem (for directed unweighted graphs) in just 2 rounds. We also prove a stronger lower bound of Ω(√n ) for the single-source shortest path problem for unweighted directed graphs that holds even when the diameter of the underlying network is 2. As far as we know this is the first lower bound that achieves Ω(√n ) for this problem.

Original languageEnglish
Title of host publication33rd International Symposium on Distributed Computing, DISC 2019
EditorsJukka Suomela
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771269
DOIs
StatePublished - Oct 2019
Event33rd International Symposium on Distributed Computing, DISC 2019 - Budapest, Hungary
Duration: 14 Oct 201918 Oct 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume146
ISSN (Print)1868-8969

Conference

Conference33rd International Symposium on Distributed Computing, DISC 2019
Country/TerritoryHungary
CityBudapest
Period14/10/1918/10/19

Keywords

  • Broadcast CONGEST
  • Distance estimation
  • Distributed algorithms
  • Small diameter

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