Counting Parameterized Border Arrays for a Binary Alphabet

  • Authors:

  • Tomohiro I;Shunsuke Inenaga;Hideo Bannai;Masayuki Takeda

  • Affiliations:

  • Department of Informatics, Kyushu University,;Graduate School of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan 819---0395;Department of Informatics, Kyushu University,;Department of Informatics, Kyushu University,

  • Venue:
  • LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
  • Year:
  • 2009

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Abstract

The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array ) is an analogue of a border array of a standard string, which is also known as the failure function of the Morris-Pratt pattern matching algorithm. In this paper we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n , where n is a a given threshold. This algorithm runs in time linear in the number of output p-border arrays.