A fast and simple algorithm for computing the longest common subsequence of run-length encoded strings

a r t i c l e i n f o a b s t r a c t Let X and Y be two strings of lengths n and m, respectively, and k and l, respectively, be the numbers of runs in their corresponding run-length encoded forms. We propose a simple algorithm for computing the longest common subsequence of two given strings X and Y in O (kl + min{p 1 , p 2 }) time, where p 1 and p 2 denote the numbers of elements in the bottom and right boundaries of the matched blocks, respectively. It improves the previously known time bound O (min{nl, km}) and outperforms the time bounds O (kl log kl) or O ((k + l + q) log(k + l + q)) for some cases, where q denotes the number of matched blocks.