Parameterized matching with mismatches

Authors:
Alberto Apostolico;Péter L. Erds;Moshe Lewenstein
Affiliations:
Department of Computer Sciences, Purdue University, West Lafayette, IN 47907, USA and Dipartimento di Ingegneria dell' Informazione, Universití di Padova, Padova, Italy;A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O. Box 127, H-1364 Hungary;Department of Computer Science, Bar-Ilan University, Ramat Gan 52900, Israel
Venue:
Journal of Discrete Algorithms
Year:
2007

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Abstract

The problem of approximate parameterized string searching consists of finding, for a given text t=t"1t"2...t"n and pattern p=p"1p"2...p"m over respective alphabets @S"t and @S"p, the injection @p"i from @S"p to @S"t maximizing the number of matches between @p"i(p) and t"it"i"+"1...t"i"+"m"-"1(i=1,2,...,n-m+1). We examine the special case where both strings are run-length encoded, and further restrict to the case where one of the alphabets is binary. For this case, we give a construction working in time O(n+(r"pxr"t)@a(r"t)log(r"t)), where r"p and r"t denote the number of runs in the corresponding encodings for y and x, respectively, and @a is the inverse of the Ackermann's function.