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 σ , 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 σ ) time using 𝒪(n^2) space.