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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
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 | ||||||||||
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| 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: |
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| 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| Status: | Not Peer Reviewed | ||||||||||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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