Efficient String Matching with k Mismatches

Given a text of length n, a pattern of length m and an integer k, we present an algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches. The algorithm runs in 0{k[mlQgTn + n) time. 1. INTEODUCTION The problem of string matching xuith k misTnatchss is defined as follows. Suppose we are given a text of length n , a pattern of length m and an integer k . Find all occurrences of the pattern in the text with at most k location in which the text and the pattern have different symbols. Note that the case fc is the extensively studied string matching problem. Let us mention a few notable algorithms for the string matching problem: linear time serial algorithms i_BM], [GS], [KMP], [KR] (a randomized algorithm) and [Y], parallel algorithms [G] and [V]. The problem has a strong pragmatical flavor. In practice, we often need to analize situations where the data is not completely reliable. SpecLfically, consider a situation where the strings which are the input for our problem contain errors and we still need to find cdl possible occurrences of the pattern in the text as m reality. Assuming some bound on the number of errors would clearly imply our problem. We present an algorithm for string matching with k m.i3matches which runs in time 0{k[mlQgm. + n)) on a random-access-machine (R^VI) [AHU]. After all the results m the present paper have been achieved, A. Slisenko has brought to our attention the paper [I] in which another algorithm for the 1. Department of Computer Science, School of Matherr.aticai Sciences, Tei Av.v university 2. Departrr.ent of Computer Science, Courant Institute of Mathematicai Sciences, N'ew York University and (present address) Department of Com.puter Science, School of Mathematical Sciences, Tei Aviv University. The research of this author was sutiTiortad by XSF grant XS?DCa-8318874 and OX?, gran: >r0014-85-K-OO46.