Parallel Computation of Combinatorial Symmetries

TL;DR

This paper introduces a novel parallel randomized algorithm for computing automorphisms of combinatorial structures, significantly improving scalability and performance over existing sequential solvers.

Contribution

The paper presents the first competitive parallel automorphism solver based on a randomized approach, outperforming current sequential tools in speed and scalability.

Findings

Achieves order-of-magnitude speedups on various graph classes

Outperforms existing sequential automorphism solvers

Demonstrates effective parallelization of the automorphism computation process

Abstract

In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the automorphism group of the constructed graph. Such solvers have been developed for over 50 years, and highly efficient sequential, single core tools are available. However no competitive parallel tools are available for the task. We introduce a new parallel randomized algorithm that is based on a modification of the individualization-refinement paradigm used by sequential solvers. The use of randomization crucially enables parallelization. We report extensive benchmark results that show that our solver is competitive to state-of-the-art solvers on a single thread, while scaling remarkably well with the use of more threads. This results in order-of-magnitude improvements on many graph classes over state-of-the-art solvers. In fact, our tool is the first parallel graph automorphism tool that outperforms current sequential tools.