Parallel Triangle Counting in Massive Streaming Graphs

TL;DR

This paper introduces a fast, cache-efficient parallel streaming algorithm for estimating the number of triangles in large, dynamic graphs, combining theoretical guarantees with empirical speedups.

Contribution

It presents a novel parallel, cache-oblivious streaming algorithm for triangle counting with proven bounds and practical efficiency improvements.

Findings

Achieves accurate triangle estimates with low memory footprint

Provides substantial speedups over sequential algorithms

Demonstrates theoretical bounds on accuracy and complexity

Abstract

The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic, we present the design and implementation of a fast and cache-efficient parallel algorithm for estimating the number of triangles in a massive undirected graph whose edges arrive as a stream. It brings together the benefits of streaming algorithms and parallel algorithms. By building on the streaming algorithms framework, the algorithm has a small memory footprint. By leveraging the paralell cache-oblivious framework, it makes efficient use of the memory hierarchy of modern multicore machines without needing to know its specific parameters. We prove theoretical bounds on accuracy, memory access cost, and parallel runtime complexity, as well as showing empirically that the algorithm yields accurate results and substantial speedups compared to an optimized sequential implementation. (This is an expanded version of a CIKM'13 paper of the same title.)