A second look at counting triangles in graph streams

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/is an element of(4.5)root T) space and outputs a (1 + is an element of) approximation of the number of triangles in the graph. This improves upon the two-pass streaming tester of Braverman et al. [2], which distinguishes between triangle-free graphs and graphs with at least T triangles using O (m/T-1/3) 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+rho) space for any constant rho >= 0. (C) 2014 Elsevier B.V. All rights reserved.