Longest common subsequence in k length substrings

Abstract

In this paper we define a new problem, motivated by computational biology, LCSk aiming at finding the maximal number of k length substrings, matching in both input string while preserving their order of appearance in the input strings. The traditional LCS definition is a spacial case of our problem, where k = 1. We provide an algorithm, solving the general case in O(n2) time, where n is the length of the input, equaling the time required for the special case of k = 1. The space requirement is O(kn). In order to enable backtracking of the solution O(n2) space is needed. © 2013 Springer-Verlag.