Approximate counting of cycles in streams

Abstract

We consider the subgraph counting problem in data streams and develop the first non-trivial algorithm for approximately counting cycles of an arbitrary but fixed size. Previous non-trivial algorithms could only approximate the number of occurrences of subgraphs of size up to six. Our algorithm is based on the idea of computing instances of complex-valued random variables over the given stream and improves drastically upon the naïve sampling algorithm. In contrast to most existing approaches, our algorithm works in a distributed setting and for the turnstile model, i. e., the input stream is a sequence of edge insertions and deletions. © 2011 Springer-Verlag Berlin Heidelberg.