Ranking and unranking bordered and unbordered words

A border of a word w is a word that is both a non-empty proper prefix and suffix of w. If w has a border, then it is said to be bordered; otherwise, it is said to be unbordered. The main results of this paper are the first algorithms to rank and unrank length-n bordered and unbordered words over a k-letter alphabet. We show that, under the unit-cost RAM model, ranking bordered and unbordered words can be done in O (kn3) time using O (n) space, and unranking them can be done in O (n4k log k) time using O (n) space. Crown Copyright (c) 2023 Published by Elsevier B.V. All rights reserved.