Graph Symmetry Detection and Canonical Labeling: Differences and Synergies

TL;DR

This paper explores the relationship between symmetry detection and canonical labeling in graphs, proposing a novel method that leverages symmetry detection to enhance canonical labeling efficiency, outperforming existing tools.

Contribution

It introduces a new approach that finds symmetries first and uses them to accelerate canonical labeling algorithms, demonstrating improved performance.

Findings

The new method outperforms state-of-the-art canonical labelers.

Symmetry detection can be effectively integrated into canonical labeling.

Empirical results confirm the efficiency gains of the proposed approach.

Abstract

Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects facilitates easy equivalence checking through quick matching. All existing canonical labeling software also finds symmetries, but the fastest symmetry-finding software does not perform canonical labeling. In this work, we contrast the two problems and dissect typical algorithms to identify their similarities and differences. We then develop a novel approach to canonical labeling where symmetries are found first and then used to speed up the canonical labeling algorithms. Empirical results show that this approach outperforms state-of-the-art canonical labelers.