Computing Maximal Repeating Subsequences in a String

In this paper we initiate the study of computing a maximal (not necessarily maximum) repeating pattern in a single input string, where the corresponding problems have been studied (e.g., a maximal common subsequence) only in two or more input strings by Hirota and Sakai starting 2019. Given an input string S of length n, we can compute a maximal square subsequence of S in O(nlog n) time, greatly improving the O(n^2) bound for computing the longest square subsequence of S. For a maximal k-repeating subsequence, our bound is O(f(k)nlog n), where f(k) is a computable function such that f(k) < k· 4^k. This greatly improves the O(n^2k-1) bound for computing a longest k-repeating subsequence of S, for k≥ 3. Both results hold for the constrained case, i.e., when the solution must contain a subsequence X of S, though with higher running times.