A New Greedy Algorithm for Longest Common Subsequence Problem

Abstract

The longest common subsequence (LCS) problem,a famous NP-Hard problem, is to find the common subsequence with maximum length on a set S of n strings of length m over an alphabet set Σ. One of important applications of this problem is to measure the similarity of biological sequence in molecular biology. This paper introduces a new algorithm for LCS problem, which uses the ant colony optimization approach and runs in O(nm4log m = Rlmn) time when m > n and m > Σ, where R denotes the number of iterations and l denotes the number of ants. Our algorithm is also a greedy algorithm based on Hamiltonian cycles. In this paper, we prove that this algorithm has performance ratio of Σ and show that the algorithm obtains better solutions than precious algorithms from our initial experimental result.