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

TL;DR

This paper presents an improved three-pass streaming algorithm for approximating the number of 4-cycles in arbitrary order insertion-only graph streams, achieving better space efficiency than previous methods.

Contribution

It introduces a novel three-pass algorithm that provides a $(1+psilon)$-approximation for 4-cycle counting with reduced space complexity in streaming models.

Findings

Achieves a space complexity of $O(rac{m \, ext{log} n}{psilon^2 T^{1/3}})$

Provides a $(1+psilon)$-approximation for 4-cycle counting

Improves over previous state-of-the-art algorithms for this problem

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.