Beyond triangles: A distributed framework for estimating 3-profiles of large graphs

Ethan R. Elenberg, Karthikeyan Shanmugam, Michael Borokhovich, Alexandros G. Dimakis

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

36 Scopus citations

Abstract

We study the problem of approximating the 3-profile of a large graph. 3-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of a large graph. Our algorithm uses the novel concept of 3-profile sparsifiers: sparse graphs that can be used to approximate the full 3-profile counts for a given large graph. Further, we study the problem of estimating local and ego 3-profiles, two graph quantities that characterize the local neighborhood of each vertex of a graph. Our algorithm is distributed and operates as a vertex program over the GraphLab PowerGraph framework. We introduce the concept of edge pivoting which allows us to collect 2-hop information without maintaining an explicit 2-hop neighborhood list at each vertex. This enables the computation of all the local 3-profiles in parallel with minimal communication. We test our implementation in several experiments scaling up to 640 cores on Amazon EC2. We find that our algorithm can estimate the 3-profile of a graph in approximately the same time as triangle counting. For the harder problem of ego 3-profiles, we introduce an algorithm that can estimate profiles of hundreds of thousands of vertices in parallel, in the timescale of minutes.

Original languageEnglish
Title of host publicationKDD 2015 - Proceedings of the 21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining
PublisherAssociation for Computing Machinery
Pages229-238
Number of pages10
ISBN (Electronic)9781450336642
DOIs
StatePublished - 10 Aug 2015
Externally publishedYes
Event21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2015 - Sydney, Australia
Duration: 10 Aug 201513 Aug 2015

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Volume2015-August

Conference

Conference21st ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2015
Country/TerritoryAustralia
CitySydney
Period10/08/1513/08/15

ASJC Scopus subject areas

  • Software
  • Information Systems

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