Periodicity algorithms for partial words

Abstract

In this paper we investigate several periodicity-related algorithms for partial words. First, we show that all periods of a partial word of length n are determined in O(n log n) time, and provide algorithms and data structures that help us answer in constant time queries regarding the periodicity of their factors. For this we need a O(n2) preprocessing time and a O(n) updating time, whenever the words are extended by adding a letter. In the second part we show that substituting letters of a word w with holes, with the property that no two holes are too close to each other, to make it periodic can be done in optimal time O(|w|). Moreover, we show that inserting the minimum number of holes such that the word keeps the property can be done as fast. © 2011 Springer-Verlag GmbH.