An Algorithm for Finding the Longest Common Almost Wave Subsequence with the Trend

Numeric sequences often exhibit similar behaviors or trends, such as fluctuations in electrocardiograms and stock values that resemble waves. This paper attempts to find the longest common almost wave subsequence with the trend (LCaWSt) between two numeric sequences A and B, given a wave trend T and a certain tolerance constant c. The LCaWSt problem aims to find the longest common subsequence of A and B, consisting of the almost increasing and decreasing segments alternatively, whose trend follows the prefix of T. We propose an algorithm for finding the LCaWSt in O(mnc) time and O(nc) space, where m and n denote the lengths of A and B, respectively, $m\ge n$.