Parameterized searching with mismatches for run-length encoded strings

  • Authors:

  • Alberto Apostolico;Péter L. Erds;Alpár Jüttner

  • Affiliations:

  • College of Computing, Georgia Institute of Technology, 801 Atlantic Drive, Atlanta, GA 30318, USA and Dipartimento di Ingegneria dell Informazione, Università di Padova Padova, Via Gradenigo ...;A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P.O. Box 127, H-1364, Hungary;Department of Operations Research, Eötvös University of Sciences, Pázmány Péter sétány 1/C, Budapest, H-1117, Hungary

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

Parameterized matching between two strings occurs when it is possible to reduce the first one to the second by a renaming of the alphabet symbols. We present an algorithm for searching for parameterized occurrences of a patten in a textstring when both are given in run-length encoded form. The proposed method extends to alphabets of arbitrary yet constant size with O(|r"p|x|r"t|) time bounds, previously achieved only with binary alphabets. Here r"p and r"t denote the number of runs in the corresponding encodings for p and t. For general alphabets, the time bound obtained by the present method exhibits a polynomial dependency on the alphabet size. Such a performance is better than applying convolution to the cleartext, but leaves the problem still open of designing an alphabet independent O(|r"p|x|r"t|) time algorithm for this problem.