Semi-local String Comparison: Algorithmic Techniques and Applications

Abstract.

Given two strings, the longest common subsequence (LCS) problem consists in computing the length of the longest string that is a subsequence of both input strings. Its generalisation, the all semi-local LCS problem, requires computing the LCS length for each string against all substrings of the other string, and for all prefixes of each string against all suffixes of the other string. We survey a number of algorithmic techniques related to the all semi-local LCS problem. We then present a number of algorithmic applications of these techniques, both existing and new. In particular, we obtain a new all semi-local LCS algorithm, with asymptotic running time matching (in the case of an unbounded alphabet) the fastest known global LCS algorithm by Masek and Paterson. We conclude that semi-local string comparison turns out to be a useful algorithmic plug-in, which unifies, and often improves on, a number of previous approaches to various substring- and subsequence-related problems.