"Tri, tri again": Finding triangles and small subgraphs in a distributed setting

Danny Dolev*, Christoph Lenzen, Shir Peled

*Corresponding author for this work

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

73 Scopus citations

Abstract

Let G = (V,E) be an n-vertex graph and M d a d-vertex graph, for some constant d. Is M d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log n) bits. A simple deterministic algorithm that requires O(n (d-2/d/log n) communication rounds is presented. For the special case that M d is a triangle, we present a probabilistic algorithm that requires an expected O(n 1/3/(t 2/3 + 1)) rounds of communication, where t is the number of triangles in the graph, and O(min{n 1/3 log 2/3 n/(t 2/3 + 1), n 1/3}) with high probability. We also present deterministic algorithms that are specially suited for sparse graphs. In graphs of maximum degree Δ, we can test for arbitrary subgraphs of diameter D in O(Δ D+1/n) rounds. For triangles, we devise an algorithm featuring a round complexity of O((A 2 log 2+n/A2 n)/n), where A denotes the arboricity of G.

Original languageEnglish
Title of host publicationDistributed Computing - 26th International Symposium, DISC 2012, Proceedings
Pages195-209
Number of pages15
DOIs
StatePublished - 2012
Event26th International Symposium on Distributed Computing, DISC 2012 - Salvador, Brazil
Duration: 16 Oct 201218 Oct 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7611 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference26th International Symposium on Distributed Computing, DISC 2012
Country/TerritoryBrazil
CitySalvador
Period16/10/1218/10/12

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