Space-Efficient STR-IC-LCS Computation

Abstract

One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of the longest common subsequence. In this paper, we address the STR-IC-LCS problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A , B , and P , if Z is one of the longest common subsequences of A and B that contains P as a substring. We present a space efficient solution for the STR-IC-LCS problem. Our algorithm computes the length of an STR-IC-LCS in O ( n 2 ) time and O (( (cid:96) + 1)( n − (cid:96) + 1)) space where (cid:96) is the length of a longest common subsequence of A and B of length n . When (cid:96) = O (1) or n − (cid:96) = O (1), then our algorithm uses only linear O ( n ) space.