Fast Algorithms for Finding the Common Subsequence of Multiple Sequences

Abstract

The longest common subsequence (LCS) algorithm is a useful method for measuring the identities and for finding similar subsequences in several sequences. Unfortunately, the longest common subsequence problem is NP-hard. In the past years, some algorithms, with several different approaches, have been proposed for finding the LCS of two given sequences. The complexity of these algorithms is about O(n2) in general and worst cases, where n is the length of sequences. When the given sequences are very long, these algorithms will take very long time and thus will become impractical. To overcome the disadvantage of time consuming, some efforts are devoted to the development of heuristic and approximate algorithms for finding the LCS. Such algorithms provide feasible solutions in practical application, such as searching in databases. However, there are few efforts for finding the LCS of more than two sequences. In this paper, we propose two approximate algorithms for finding the LCS of multiple sequences. The time complexity of our algorithms are O(kn) and O(2kn + 3n), where  is the size of symbol set, k and n are the number and length of input sequences, respectively. In the experimental results, our algorithm finds the common subsequences whose lengths are about 0.8|LCS| in average for two random sequences with uniform distribution. In the rank-identity experimental result, it shows that our methods are suitable in practical application.