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 $p \geq \max{ (\frac{ \Delta \log{ n}}{ t}, \frac{ \log{ n}}{ \sqrt{ t}})}$, 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 \epsilon \Mean{ T}} = o(1)$. Finally, we present a \textsc{ MapReduce} implementation of our algorithm.
Categories: cs.DS cs.DM cs.SI