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 ? 4.5 T ) space and outputs a (1+?) ( 1 + ? ) 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 T 1 / 2 + ? ) space for any constant ??0 ? ? 0 .
graphs data streams randomized algorithms