The k-Centre Problem for Classes of Cyclic Words

Abstract

A subsequence of a word w is a word u such that u = wA word w is k-subsequence universal over an alphabet Σ if every word in Σ k appears in w as a subsequence. In this paper, we provide new algorithms for k-subsequence universal words of fixed length n over the alphabet Σ = {1, 2, . . . , σ}. Letting U(n, k, σ) denote the set of n-length k-subsequence universal words over Σ, we provide:• an O(nkσ) time algorithm for counting the size of U(n, k, σ);• an O(nkσ) time algorithm for ranking words in the set U(n, k, σ);• an O(nkσ) time algorithm for unranking words from the set U(n, k, σ);• an algorithm for enumerating the set U(n, k, σ) with O(nσ) delay after O(nkσ) preprocessing.