Computing Minimal and Maximal Suffixes of a Substring Revisited

Abstract

We revisit the problems of computing the maximal and the minimal non-empty suffixes of a substring of a longer text of length n, introduced by Babenko, Kolesnichenko and Starikovskaya [CPM’13]. For the minimal suffix problem we show that for any 1 ≤ τ ≤ logn there exists a linear-space data structure with $\mathcal{O}(\tau)$ query time and $\mathcal{O}(n \log n / \tau)$ preprocessing time. As a sample application, we show that this data structure can be used to compute the Lyndon decomposition of any substring of the text in $\mathcal{O}(k \tau)$ time, where k is the number of distinct factors in the decomposition. For the maximal suffix problem we give a linear-space structure with $\mathcal{O}(1)$ query time and $\mathcal{O}(n)$ preprocessing time, i.e., we manage to achieve both the optimal query and the optimal construction time simultaneously.