On String Matching with Mismatches

In this paper, we consider several variants of the pattern matching with mismatches problem. In particular, given a text \(T=t_1 t_2\cdots t_n\) and a pattern \(P=p_1p_2\cdots p_m\), we investigate the following problems: (1) pattern matching with mismatches: for every \(i, 1\leq i \leq n-m+1\) output, the distance between \(P\) and \(t_i t_{i+1}\cdots t_{i+m-1}\); and (2) pattern matching with \(k\) mismatches: output those positions \(i\) where the distance between \(P\) and \(t_i t_{i+1}\cdots t_{i+m-1}\) is less than a given threshold \(k\). The distance metric used is the Hamming distance. We present some novel algorithms and techniques for solving these problems. We offer deterministic, randomized and approximation algorithms. We consider variants of these problems where there could be wild cards in either the text or the pattern or both. We also present an experimental evaluation of these algorithms. The source code is available at http://www.engr.uconn.edu/\(\sim\)man09004/kmis.zip