A New Algorithm for Generating

In this paper we present an algorithm for generating the lexicographi-cally smallest representatives of all the n-bead necklaces in k-colors. The time required is O(nN n k), where N n k is the number of necklaces with n beads of k colors. To our knowledge, this is the rst algorithm for this problem which has been proved to asymptotically improve the obvious O(n k n) approach of examining all k-ary n-tuples and rejecting those which are not lexicographically smallest rotations. Our algorithm has another advantage over a competitive one proposed by Fredericksen, Kessler, and Maiorana in that it can be implemented so that there is a gap of at most one non-necklace examined between any two necklaces generated, whereas the FKM algorithm can have gaps as large as b(n ? 1)=2c. Although no good upper bound was established for FKM, we show experimentally that its performance appears to be as least as good as ours for k > 2.