A fast algorithm for computing a longest common increasing subsequence

Let A = 〈a1, a2, . . . , am〉 and B = 〈b1, b2, . . . , bn〉 be two sequences, where each pair of elements in the sequences is comparable. A common increasing subsequence of A and B is a subsequence 〈ai1 = bj1 , ai2 = bj2 , . . . , ail = bjl 〉, where i1 < i2 < · · · < il and j1 < j2 < · · · < jl , such that for all 1 k < l, we have aik < aik+1 . A longest common increasing subsequence of A and B is a common increasing subsequence of the maximum length. This paper presents an algorithm for delivering a longest common increasing subsequence in O(mn) time and O(mn) space.  2004 Elsevier B.V. All rights reserved.