Longest Square Subsequence Problem Revisited

The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length $n$ can be computed using $O(n^2)$ time [Kosowski 2004], or with (model-dependent) polylogarithmic speed-ups using $O(n^2 (\log \log n)^2 / \log^2 n)$ time [Tiskin 2013]. We present the first algorithm for LSS whose running time depends on other parameters, i.e., we show that an LSS of $S$ can be computed in $O(r\min \{n,M\}\log \frac{n}{r}+n+M\log n)$ time with $O(M)$ space, where $r$ is the length of an LSS of $S$ and $M$ is the number of matching points on $S$.