Longest bordered and periodic subsequences

We present an algorithm computing the longest periodic subsequence of a string of length n in O(n7) time with O(n3) space. We obtain improvements when restricting the exponents or extending the search allowing the reported subsequence to be subperiodic down to O(n2) time and O(n) space. By allowing subperiodic subsequences in the output, the task becomes finding the longest bordered subsequence, for which we devise a conditional lower bound. (c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).