finding the smallest image of a set
We describe an algorithm for finding a canonical image of a set of points under the action of a permutation group. Specifically if we order images by sorting them and ordering the resulting sequences lexicographically, we find the first image. This has applications to combinatorial and other search problems, allowing isomorphic results to be eliminated more efficiently.We give worst-case asymptotic running time estimates and practical results obtained with a GAP implementation.
smallest image algorithm permutation group