New refiners for permutation group search

TL;DR

This paper introduces orbital graphs to enhance permutation group algorithms, significantly improving practical performance for problems like intersection and stabilizer computations through integration with partition backtracking.

Contribution

It presents novel methods for incorporating orbital graphs into existing algorithms, leading to substantial efficiency gains in permutation group problem solving.

Findings

Algorithms show several orders of magnitude speedup in practice

Orbital graphs improve the efficiency of intersection and stabilizer computations

Integration with partition backtracking enhances overall algorithm performance

Abstract

We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition backtracking, the current state of the art algorithm for many permutation group problems. We then show how our algorithms perform in practice, demonstrating improvements of several orders of magnitude for some problems.