# A 2D Parallel Triangle Counting Algorithm for Distributed-Memory Architectures

## TL;DR

This paper introduces a scalable 2D parallel triangle counting algorithm for distributed-memory systems, optimizing communication and computation to handle large graphs efficiently.

## Contribution

The paper presents a novel 2D cyclic decomposition-based distributed triangle counting algorithm with key optimizations for sparsity and reduced memory overhead.

## Key findings

- Achieves 3.24 to 7.22 speedup over baseline with 169 MPI ranks
- Attains an average speedup of 10.2 times compared to previous algorithms
- Effectively handles large synthetic and real-world graphs

## Abstract

Triangle counting is a fundamental graph analytic operation that is used extensively in network science and graph mining. As the size of the graphs that needs to be analyzed continues to grow, there is a requirement in developing scalable algorithms for distributed-memory parallel systems. To this end, we present a distributed-memory triangle counting algorithm, which uses a 2D cyclic decomposition to balance the computations and reduce the communication overheads. The algorithm structures its communication and computational steps such that it reduces its memory overhead and includes key optimizations that leverage the sparsity of the graph and the way the computations are structured. Experiments on synthetic and real-world graphs show that our algorithm obtains an average relative speedup that range between 3.24 and 7.22 out of 10.56 across the datasets using 169 MPI ranks over the performance achieved by 16 MPI ranks. Moreover, we obtain an average speedup of 10.2 times on comparison with previously developed distributed-memory parallel algorithms.