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. © 2006 Elsevier B.V. All rights reserved.