Computing canonical images in permutation groups with Graph Backtracking

TL;DR

This paper introduces a novel algorithm for computing canonical images in permutation groups using Graph Backtracking, extending existing frameworks and generalizing prior algorithms like Nauty.

Contribution

The paper presents a new algorithm that enhances the computation of canonical images in permutation groups by building on and generalizing previous graph backtracking methods.

Findings

Algorithm extends Graph Backtracking framework.

Generalizes Nauty and Minimal image algorithms.

Provides a new approach for permutation group computations.

Abstract

We describe a new algorithm for finding a canonical image of an object under the action of a finite permutation group. This algorithm builds on previous work using Graph Backtracking, which extends Jeffrey Leon's Partition Backtrack framework. Our methods generalise both Nauty and Steve Linton's Minimal image algorithm.