Papers › Longest Common Subsequence in k-length substrings
Longest Common Subsequence in k-length substrings
Gary Benson, Avivit Levy, Riva Shalom
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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(n²) 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). %, however, in order to enable %backtracking of the solution, O(n²) space is needed. 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.
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