Longest common subsequence problem for run-length-encoded strings

In this paper, we present a new and efficient algorithm for solving the longest common subsequence problem between two run-length-encoded (RLE) strings. Suppose Ŷ and X are two RLE strings having length k and ℓ, respectively. Also, assume that Y and X are the two uncompressed versions of the two RLE strings Ŷ and X having length k and ℓ respectively. Then, our algorithm runs in O((k + ℓ)+R loglog(kℓ) + R log log ω) time, where ω = k + ℓ and R is the total number of ordered pairs of positions at which the two RLE strings match. Our algorithm outperforms the best algorithms for the same problem in the literature.