Parallelizing Maximal Clique Enumeration on GPUs

TL;DR

This paper introduces a GPU-based method for exact maximal clique enumeration that uses depth-first traversal and dynamic load balancing, significantly outperforming previous CPU-based approaches and enabling scalable multi-GPU execution.

Contribution

It proposes a novel GPU parallelization strategy for MCE using depth-first traversal, load balancing, and memory-efficient representations, advancing the state-of-the-art in scalability and performance.

Findings

GPU implementation outperforms CPU by 4.9x on average

Scales efficiently to multiple GPUs

Open-sourced code for further research

Abstract

We present a GPU solution for exact maximal clique enumeration (MCE) that performs a search tree traversal following the Bron-Kerbosch algorithm. Prior works on parallelizing MCE on GPUs perform a breadth-first traversal of the tree, which has limited scalability because of the explosion in the number of tree nodes at deep levels. We propose to parallelize MCE on GPUs by performing depth-first traversal of independent subtrees in parallel. Since MCE suffers from high load imbalance and memory capacity requirements, we propose a worker list for dynamic load balancing, as well as partial induced subgraphs and a compact representation of excluded vertex sets to regulate memory consumption. Our evaluation shows that our GPU implementation on a single GPU outperforms the state-of-the-art parallel CPU implementation by a geometric mean of 4.9x (up to 16.7x), and scales efficiently to multiple GPUs. Our code has been open-sourced to enable further research on accelerating MCE.