Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-11-20 , DOI: 10.1016/j.tcs.2020.11.035 Toan Thang Ta; Yi-Kung Shieh; Chin Lung Lu
Given a positive constant c, a sequence of k numbers is said to be almost increasing if and only if for all . A longest common almost-increasing subsequence (LCaIS) between two input sequences is a longest common subsequence that is also an almost increasing sequence. We found out that the existing algorithm proposed by Moosa et al.  to find an LCaIS of two sequences without repeated elements gives an incorrect result for some instances. In this work, we present a dynamic programming algorithm that can correctly compute an LCaIS between any two sequences with repeated elements in time and space, where n and m are the lengths of two input sequences and l is the length of the output LCaIS.