Finding Maximal Quasiperiodicities in Strings

Abstract

Apostolico and Ehrenfeucht defined the notion of a maximal quasiperiodic
substring and gave an algorithm that finds all maximal quasiperiodic
substrings in a string of length n in time O(n log2 n). In this paper we
give an algorithm that finds all maximal quasiperiodic substrings in a
string of length n in time O(n log n) and space O(n). Our algorithm uses
the suffix tree as the fundamental data structure combined with efficient
methods for merging and performing multiple searches in search trees.
Besides finding all maximal quasiperiodic substrings, our algorithm also
marks the nodes in the suffix tree that have a superprimitive path-label.