Engineering a Fast Probabilistic Isomorphism Test

TL;DR

This paper introduces a new probabilistic Monte-Carlo algorithm for graph isomorphism testing that implicitly exploits symmetries, outperforming existing deterministic methods in speed and asymptotic behavior on standard benchmarks.

Contribution

The paper presents a novel probabilistic algorithm that implicitly leverages symmetries, achieving superior performance over all existing solutions for graph isomorphism testing.

Findings

Outperforms all state-of-the-art isomorphism solvers on standard benchmarks.

Achieves an order of magnitude faster running times on many input types.

Demonstrates better asymptotic behavior compared to deterministic algorithms.

Abstract

We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive benchmarks, showing that the algorithm outperforms all state-of-the-art solutions for isomorphism testing on most inputs from the de facto standard benchmark library for isomorphism testing. On many input types, our data not only show improved running times by an order of magnitude, but also reflect a better asymptotic behavior. Our results demonstrate that, with current algorithms, isomorphism testing is in practice easier than the related problems of computing the automorphism group or canonically labeling a graph. The results also show that probabilistic algorithms for isomorphism testing can be engineered to outperform deterministic approaches, even asymptotically.