Algorithms for computing variants of the longest common subsequence problem

The longest common subsequence(LCS) problem is one of the classical and wellstudied problems in computer science. The computation of the LCS is a frequent task in DNA sequence analysis, and has applications to genetics and molecular biology. In this paper we introduce new variants of LCS problem and present efficient algorithms to solve them. In particular we introduce the notion of gap-constraints in the LCS problems. For the LCS problem with fixed gap, we first present a naive algorithm runs in O(n2 + R(K + 1)2) time, where R is the total number of ordered pairs of positions at which the two strings match and K is the fixed gap-constraint. We then improve the running time to O(n2 + RK + R log log n) using some novel techniques. Furthermore, we present an algorithm that is independent of K and runs in O(n2 + R log log n) time. Using these techniques, we also present a new O(n2) algorithm to solve the original LCS problem. Additionally, we modify our algorithms to handle elastic and r...

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Costas S. Iliopoulos, M. Sohel Rahman
• Keywords: Algorithm, LCS Problem, Longest Common Subsequence, TCS 2008, Theoretical Computer Science