A New Algorithm for Generating Necklaces
نویسندگان
چکیده
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 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 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 c Although no good upper bound was established for FKM we show experimentally that its perfor mance appears to be as least as good as ours for k
منابع مشابه
Fast Algorithms to Generate Necklaces, Unlabeled Necklaces, and Irreducible Polynomials over GF(2)
Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an Ž . equivalence class of k-ary strings under rotation the cyclic group . A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algoŽ . rit...
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