Verifying a parameterized border array in O(n1.5) time

  • Authors:

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

  • Affiliations:

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

  • Venue:
  • CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
  • Year:
  • 2010

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Abstract

The parameterized pattern matching problem is to check if there exists a renaming bijection on the alphabet with which a given pattern can be transformed into a substring of a given text. A parameterized border array (p-border array) is a parameterized version of a standard border array, and we can efficiently solve the parameterized pattern matching problem using p-border arrays. In this paper we present an O(n1.5)-time O(n)-space algorithm to verify if a given integer array of length n is a valid p-border array for an unbounded alphabet. The best previously known solution takes time proportional to the n-th Bell number 1/eΣk=0∞kn/k!, and hence our algorithm is quite efficient.