Faster STR-IC-LCS Computation via RLE

The constrained LCS problem asks one to find a longest common subsequence of two input strings A and B with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given constraint string C as a substring. Given two strings A and B of respective lengths M and N , and a constraint string C of length at most min{M,N}, the best known algorithm for the STR-IC-LCS problem, proposed by Deorowicz (Inf. Process. Lett., 11:423–426, 2012), runs in O(MN) time. In this work, we present an O(mN+nM)time solution to the STR-IC-LCS problem, where m and n denote the sizes of the run-length encodings of A and B, respectively. Since m ≤ M and n ≤ N always hold, our algorithm is always as fast as Deorowicz’s algorithm, and is faster when input strings are compressible via RLE. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems