A space efficient algorithm for the longest common subsequence in k-length substrings

Two space efficient algorithms to solve the LCSk problem and LCS(>=)k problem are presented in this paper. The algorithms improve the time and space complexities. of the algorithms of Benson et al. [4]. The space cost of the first algorithm to solve the LCSk problem is reduced from O (n(2)) to O (kn), if the size of the two input sequences are both n. The time and space costs of the second algorithm to solve the LCS >= k problem are both improved. The time cost is reduced from O (kn(2)) to O (n(2)), and the space cost is reduced from O (n(2)) to O (kn). In the case of k = O(1), the two algorithms are both linear space algorithms. (C) 2017 Elsevier B.V. All rights reserved.