Improved 3-pass Algorithm for Counting 4-cycles in Arbitrary Order Streaming

Abstract

The problem of counting small subgraphs, and specifically cycles, in the streaming model received a lot of attention over the past few years. In this paper, we consider arbitrary order insertion-only streams, improving over the state-of-the-art result on counting 4-cycles. Our algorithm computes a $(1+\epsilon )$-approximation by taking three passes over the stream and using space $O(\frac{m\log n}{{\epsilon }^2{T}^{1/3}})$, where $m$ is the number of edges in the graph and $T$ is the number of 4-cycles.