A Comparative Study of Different Longest Common Subsequence Algorithms

The longest common subsequence is a classical problem which is solved by using the dynamic programming approach. The LCS problem has an optimal substructure: the problem can be broken down into smaller, simple "subproblems", which can be broken down into yet simpler subproblems, and so on, until, finally, the solution becomes trivial. The LCS problem also has overlapping subproblems: the solution to a higher subproblem depends on the solutions to several of the lower subproblems. Problems with these two properties—optimal substructure and overlapping subproblems—can be approached by a problem-solving technique called dynamic programming, in which the solution is built up starting with the simplest subproblems. The LCS in computer science is used approximate string matching. The approximate string matching is the technique of finding strings that match a pattern approximately (rather than exactly). Most often when we need to match a pattern exact matching is not possible, due to insufficient data, broken data, or other such reasons. So we try to find a close match instead of an exact match. And for this we need to Longest Common Subsequence (LCS). Different LCS algorithms have been made and we will try to analyze some of these algorithms. Keywords— Dynamic Programming, Longest Common Subsequence, Pattern Matching , Space and Time Complexity.