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 = t1t2 · · · tn and a pattern P = p1p2 · · · pm, we investigate the following problems: (1) pattern matching with mismatches: for every i, 1 ≤ i ≤ n −m + 1 output, the distance between P and titi+1 · · · ti+m−1; and (2) pattern matching with k mismatches: output those positions i where the distance between P and titi+1 · · · ti+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/∼man09004/kmis.zip.