A linear space algorithm for computing a longest common increasing subsequence

Let X and Y be sequences of integers. A common increasing subsequence of X and Y is an increasing subsequence common to X and Y. In this note, we propose an O(|X|⋅|Y|)-time and O(|X|+|Y|)-space algorithm for finding one of the longest common increasing subsequences of X and Y, which improves the space complexity of Yang et al. [I.H. Yang, C.P. Huang, K.M. Chao, A fast algorithm for computing a longest common increasing subsequence, Inform. Process. Lett. 93 (2005) 249–253] O(|X|⋅|Y|)-time and O(|X|⋅|Y|)-space algorithm, where |X| and |Y| denote the lengths of X and Y, respectively.