Colorful Triangle Counting and a MapReduce Implementation

Abstract

In this note we introduce a new randomized algorithm for counting triangles in graphs. We show that under mild conditions, the estimate of our algorithm is strongly concentrated around the true number of triangles. Specifically, if $p\ge \max (\frac{\Delta \log n}{t},\frac{\log n}{\sqrt{t}})$, where $n$, $t$, $\Delta$ denote the number of vertices in $G$, the number of triangles in $G$, the maximum number of triangles an edge of $G$ is contained, then for any constant $\epsilon >0$ our unbiased estimate $T$ is concentrated around its expectation, i.e., $ \Prob{|T - \Mean{T}| \geq ε\Mean{T}} = o(1)$. Finally, we present a \textsc{MapReduce} implementation of our algorithm.

8 pages, 1 figure

Cited by in corpus (1)

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