Conflict Anticipation in the Search for Graph Automorphisms

TL;DR

This paper introduces a novel simultaneous refinement technique for graph automorphism algorithms, significantly improving efficiency by anticipating conflicts and achieving exponential speedups on challenging graph families.

Contribution

It presents a new simultaneous refinement method that enhances conflict anticipation in graph automorphism search algorithms, outperforming previous approaches.

Findings

Exponential speedup on Miyazaki graphs

Effective conflict anticipation reduces runtimes

Improved pruning leads to faster automorphism detection

Abstract

Effective search for graph automorphisms allows identifying symmetries in many discrete structures, ranging from chemical molecules to microprocessor circuits. Using this type of structure can enhance visualization as well as speed up computational optimization and verification. Competitive algorithms for the graph automorphism problem are based on efficient partition refinement augmented with group-theoretic pruning techniques. In this paper, we improve prior algorithms for the graph automorphism problem by introducing simultaneous refinement of multiple partitions, which enables the anticipation of future conflicts in search and leads to significant pruning, reducing overall runtimes. Empirically, we observe an exponential speedup for the family of Miyazaki graphs, which have been shown to impede leading graph-automorphism algorithms.