Computing Maximal Repeating Subsequences in a String

arXiv:2601.12200v1 Announce Type: new
Abstract: 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 $f(k) < kcdot 4^k$. This greatly improves the $O(n^{2k-1})$ bound for computing a longest $k$-repeating subsequence of $S$, for $kgeq 3$. Both results hold for the constrained case, i.e., when the solution must contain a subsequence $X$ of $S$, though with higher running times.