Graph explorer

Substring Suffix Selection

We study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal suffix of a string, which is a basic ingredient in many other problems. We first revisit two special cases of the problem, introduced by Babenko, Kolesnichenko and Starikovskaya [CPM&#39;13], in which we are asked to compute the minimal non-empty and the maximal suffixes of a substring. For the maximal suffixes problem, we give a linear-space structure with O(1) query time and linear preprocessing time, i.e., we manage to achieve optimal construction and optimal query time simultaneously. For the minimal suffix problem, we give a linear-space data structure with O(τ) query time and O(n log n / τ) preprocessing time, where 1 <= τ<= log n is a parameter of the data structure. As a sample application, we show that this data structure can be used to compute the Lyndon decomposition of any substring of T in O(k τ) time, where k is the number of distinct factors in the decomposition. Finally, we move to the general case of the substring suffix selection