PERFORMANCE ANALYSIS OF SOME SIMPLE HEURISTICS FOR COMPUTING LONGEST COMMON SUBSEQUENCES

Although the Longest Common Subsequence (LCS) Problem has been studied by many researchers for years, heuristic methods have not been invest igated before. In this paper we present a simple heuristic which guara ntees to return a common subsequence of length at least 1/s that of th e longest where s is the number of different symbols in the input stri ngs. Furthermore, we generalize the idea to several classes of heurist ic algorithms. Surprisingly, we find that no other heuristic in these classes outperforms this simple algorithm. In other words, we show tha t any heuristic which uses only global information, such as number of symbol occurrences, might return a common subsequence as short as 1/s of the length of the longest. Analysis of the average performance of t he simple heuristic for s = 2 is also presented.