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. Keywords permutation group, algorithm, smallest image General Terms Algorithms Categories and Subject Descriptors F [2]: 2; G [2]: 1; I [1]: 2

• Type: Conference
• Year: 2004
• Where: ISSAC
• Authors: Steve Linton
• Keywords: ISSAC 2004, Keywords Permutation Group, Permutation Group, Worst-case Asymptotic Running