Date of Original Version

11-2010

Type

Conference Proceeding

Rights Management

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-18009-5_3

Abstract or Description

In this paper we present an efficient triangle counting algorithm which can be adapted to the semistreaming model [12]. The key idea of our algorithm is to combine the sampling algorithm of [31,32] and the partitioning of the set of vertices into a high degree and a low degree subset respectively as in [1], treating each set appropriately. We obtain a running time O(m+m3/2Δlogntϵ2) and an ε approximation (multiplicative error), where n is the number of vertices, m the number of edges and Δ the maximum number of triangles an edge is contained. Furthermore, we show how this algorithm can be adapted to the semistreaming model with space usage O(m1/2logn+m3/2Δlogntϵ2) and a constant number of passes (three) over the graph stream. We apply our methods in various networks with several millions of edges and we obtain excellent results. Finally, we propose a random projection based method for triangle counting and provide a sufficient condition to obtain an estimate with low variance.

DOI

10.1007/978-3-642-18009-5_3

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Published In

Lecture Notes in Computer Science, 6516, 15-24.