Computing Longest Lyndon Subsequences and Longest Common Lyndon Subsequences

Given a string T of length n whose characters are drawn from an ordered alphabet of size s, its longest Lyndon subsequence is a maximum-length subsequence of T that is a Lyndon word. We propose algorithms for finding such a subsequence in O(n(3)) time with O(n) space, or online in O(n(3)) space and time. Our first result can be extended to find the longest common Lyndon subsequence of two strings of length at most n in O (n(4 )s) time using O(n(2)) space.