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A second look at counting triangles in graph streams

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Cormode, Graham and Jowhari, Hossein (2014) A second look at counting triangles in graph streams. Theoretical Computer Science, Volume 552 . pp. 44-51. doi:10.1016/j.tcs.2014.07.025

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Official URL: http://dx.doi.org/10.1016/j.tcs.2014.07.025

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Abstract

In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with m edges and at least T triangles, we show that an extra look over the stream yields a two-pass streaming algorithm that uses O((m)/(ε4.5sqrt(T))) space and outputs a (1+ε) approximation of the number of triangles in the graph. This improves upon the two-pass streaming tester of Braverman, Ostrovsky and Vilenchik, ICALP 2013, which distinguishes between triangle-free graphs and graphs with at least T triangle using O((m)/(T1/3)) space. Also, in terms of dependence on T, we show that more passes would not lead to a better space bound. In other words, we prove there is no constant pass streaming algorithm that distinguishes between triangle-free graphs from graphs with at least T triangles using O((m)/(T1/2+ρ)) space for any constant ρ>=0.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Triangle, Graph algorithms, Graph theory, Combinatorial analysis
Journal or Publication Title: Theoretical Computer Science
Publisher: Elsevier Science BV
ISSN: 0304-3975
Official Date: 2 October 2014
Dates:
DateEvent
2 October 2014Published
19 August 2014Available
31 July 2014Accepted
4 January 2014Submitted
Volume: Volume 552
Number of Pages: 8
Page Range: pp. 44-51
DOI: 10.1016/j.tcs.2014.07.025
Status: Not Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Embodied As: 1
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