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 | ṡ | 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 | ṡ | Y |)-time and O (| X | ṡ | Y |)-space algorithm, where | X | and | Y | denote the lengths of X and Y, respectively.