Parameterized matching with mismatches

The problem of approximate parameterized string searching consists of finding, for a given text t = t1t2 . . . tn and pattern p = p1p2 . . . pm over respective alphabets Σt and Σp , the injection πi from Σp to Σt maximizing the number of matches between πi(p) and ti ti+1 . . . ti+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+ (rp × rt )α(rt ) log(rt )), where rp and rt denote the number of runs in the corresponding encodings for y and x, respectively, and α is the inverse of the Ackermann’s function. © 2006 Elsevier B.V. All rights reserved.