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 titi+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.

• Type: Journal
• Year: 2007
• Where: JDA
• Authors: Alberto Apostolico, Péter L. Erdös, Moshe Lewenstein
• Keywords: Approximate Parameterized String, Injection πi, JDA 2007, Respective Alphabets Σt