Computing Minimal and Maximal Suffixes of a Substring Revisited

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 O(τ) query time and O(n logn/τ) 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 O(kτ) time, where k is the number of distinct factors in the decomposition. For the maximal suffix problem we give a linearspace structure with O(1) query time and O(n) preprocessing time, i.e., we manage to achieve both the optimal query and the optimal construction time simultaneously.