Computing Longest (Common) Lyndon Subsequences

Abstract: Given a string $T$ with length $n$ whose characters are drawn from an ordered alphabet of size $\sigma$, its longest Lyndon subsequence is a longest subsequence of $T$ that is a Lyndon word. We propose algorithms for finding such a subsequence in $O(n<sup>3)$ time with $O(n)$ space, or online in $O(n³ \sigma)$ space and time. Our first result can be extended to find the longest common Lyndon subsequence of two strings of length $n$ in $O(n⁴ \sigma)$ time using $O(n<sup>3)$ space.