Possibilities and impossibilities for distributed subgraph detection

Orr Fischer, Fabian Kuhn, Tzlil Gonen, Rotem Oshman

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

Abstract

In the distributed subgraph detection problem, we are given a fixed subgraph H, and the network must decide whether the network graph contains a copy of H or not. Subgraph detection can be solved in a constant number of rounds if message size is unbounded, but in the CONGEST model, where each message has bounded size, it can have high round complexity. Distributed subgraph detection has received significant attention recently, with new upper and lower bounds, but several fundamental questions remain open. In this paper we prove new possibility and impossibility results for subgraph detection in the CONGEST model. We show for the first time that some subgraphs require superlinear — in fact, nearly quadratic — running time, even in small-diameter networks. We also study cycle-detection, and show that any even cycle can be detected in sublinear time (in contrast to odd cycles, which require linear time). For the special case of triangle-detection, we show that deterministic algorithms require Ω(log n) total communication even in graphs of degree 2, and that one-round randomized algorithms must send Ω(∆) bits in graphs of degree ∆, improving on the recent results of [Abboud et. al.]. Finally, we extend a recent lower bound of [Izumi, Le Gall] on listing all triangles to cliques of any size.

Original languageEnglish
Title of host publicationSPAA 2018 - Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures
Pages153-162
Number of pages10
ISBN (Electronic)9781450357999
DOIs
StatePublished - 11 Jul 2018
Event30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018 - Vienna, Austria
Duration: 16 Jul 201818 Jul 2018

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference30th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2018
Country/TerritoryAustria
CityVienna
Period16/07/1818/07/18

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

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