Counting arbitrary subgraphs in data streams

Abstract

We study the subgraph counting problem in data streams. We provide the first non-trivial estimator for approximately counting the number of occurrences of an arbitrary subgraph H of constant size in a (large) graph G. Our estimator works in the turnstile model, i.e., can handle both edge-insertions and edge-deletions, and is applicable in a distributed setting. Prior to this work, only for a few non-regular graphs estimators were known in case of edge-insertions, leaving the problem of counting general subgraphs in the turnstile model wide open. We further demonstrate the applicability of our estimator by analyzing its concentration for several graphs H and the case where G is a power law graph. © 2012 Springer-Verlag Berlin Heidelberg.