Fast Algorithms for Computing the Constrained LCS of Run-Length Encoded Strings

In the constrained longest common subsequence (CLCS) problem, we are given two sequences X , Y and the constrained sequence P in run-length encoded (RLE) format, where |X| = n, |Y | = m and |P | = r and the numbers of runs in RLE format are N , M and R, respectively. In this paper, we show that after the sequences are encoded, the CLCS problem can be solved in O(NMr+ r × min{q1, q2} + q3) time, where q1 and q2 denote the numbers of elements in the bottom and right boundaries of the partially matched blocks on the first layer, and q3 denotes the number of elements of whole boundaries of all fully matched cuboids in the DP lattice. If the compression ratio is good, our work obviously outperforms the previously known DP algorithm and the Hunt-and-Szymanski-like algorithm.