Longest Common Subsequence in k Length Substrings

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 strings while preserving their order of appearance. The traditional LCS definition is a special case of our problem, where k = 1. We provide an algorithm, solving the general case in O(n) time, where n is the length of the input strings, equaling the time required for the special case of k = 1. The space requirement of the algorithm is O(kn). We also define a complementary EDk distance measure and show that EDk(A,B) can be computed in O(nm) time and O(km) space, where m, n are the lengths of the input sequences A and B respectively.