Resequencing a Set of Strings Based on a Target String

Given a set S ={ S 1 , S 2 ,…, S l } of l strings, a text T , and a natural number k , find a string M , which is a concatenation of k strings (not necessarily distinct, i.e., a string in S may occur more than once in M ) from S , whose longest common subsequence with T is largest, where a string in S may occur more than once in M . Such a string is called a k -inlay. The resequencing longest common subsequence problem (resequencing LCS problem for short) is to find a k -inlay for each query with parameter k after T and S are given. In this paper, we propose an algorithm for solving this problem which takes O ( nml ) preprocessing time and O ( ϑ k k ) query time for each query with parameter k , where n is the length of T , m is the maximal length of strings in S , and ϑ k is the length of the longest common subsequence between a k -inlay and T .