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

Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)

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/e Σk=0 kn/k! , and hence our algorithm is quite efficient.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 21st Annual Symposium, CPM 2010, Proceedings
PublisherSpringer Verlag
Pages238-250
Number of pages13
ISBN (Print)3642135080, 9783642135088
DOIs
Publication statusPublished - Jan 1 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6129
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    I, T., Inenaga, S., Bannai, H., & Takeda, M. (2010). Verifying a parameterized border array in O(n1.5) time. In Combinatorial Pattern Matching - 21st Annual Symposium, CPM 2010, Proceedings (pp. 238-250). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6129). Springer Verlag. https://doi.org/10.1007/978-3-642-13509-5_22