Minimal and Canonical Images

Abstract

We describe a family of new algorithms for finding the canonical image of a set of points under the action of a permutation group. This family of algorithms makes use of the orbit structure of the group, and a chain of subgroups of the group, to efficiently reduce the amount of search which must be performed to find a canonical image. We present both a formal proof of correctness of our algorithms and experiments on different permutation groups, which compare our algorithms with the previous state of the art.