Approximate string matching in sublinear expected time

Abstract

The k differences approximate string matching problem specifies a text string of length n, a pattern string of length m, and the number k of differences (insertions, deletions, substitutions) allowed in a match, and asks for every location in the text where a match occurs. Previous algorithms required at least O(nk) time. When k is as large as a fraction of m, no substantial progress has been made over O(nm) dynamic programming. The authors have investigated much faster algorithms for restricted cases of the problem, such as when the text string is random and errors are not too frequent. They have devised an algorithm that, for k>