Constrained Longest Common Subsequences with Run-Length-Encoded Strings

Given two strings X and Y and a constraining string P, a string Z is called a constrained longest common subsequence of X and Y with respect to P if Z is the longest common subsequence of X and Y such that P is a subsequence of Z. In this paper, we propose an O(r x min{mN, nM})-time algorithm for solving this problem, where m, n and r are the lengths of X, Y and P, respectively, and M and N are the number of runs of the run-length-encoded strings of X and Y, respectively.