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)


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
Number of pages13
ISBN (Print)3642135080, 9783642135088
Publication statusPublished - 2010

Publication series

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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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