International Symposium on String Processing and Information Retrieval

SPIRE 2015: String Processing and Information Retrieval pp 124-136 | Cite as

A Faster Algorithm for Computing Maximal \(\alpha \)-gapped Repeats in a String

  • Yuka Tanimura
  • Yuta Fujishige
  • Tomohiro I
  • Shunsuke Inenaga
  • Hideo Bannai
  • Masayuki Takeda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9309)

Abstract

A string \(x = uvu\) with both uv being non-empty is called a gapped repeat with period \(p = |uv|\), and is denoted by pair (xp). If \(p \le \alpha (|x|-p)\) with \(\alpha > 1\), then (xp) is called an \(\alpha \) -gapped repeat. An occurrence \([i, i+|x|-1]\) of an \(\alpha \)-gapped repeat (xp) in a string w is called a maximal \(\alpha \)-gapped repeat of w, if it cannot be extended either to the left or to the right in w with the same period p. Kolpakov et al. (CPM 2014) showed that, given a string of length n over a constant alphabet, all the occurrences of maximal \(\alpha \)-gapped repeats in the string can be computed in \(O(\alpha ^2 n + occ )\) time, where \( occ \) is the number of occurrences. In this paper, we propose a faster \(O(\alpha n + occ )\)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of \(\alpha \).

Keywords

Brodal 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yuka Tanimura
    • 1
  • Yuta Fujishige
    • 1
  • Tomohiro I
    • 2
  • Shunsuke Inenaga
    • 1
  • Hideo Bannai
    • 1
  • Masayuki Takeda
    • 1
  1. 1.Department of InformaticsKyushu UniversityFukuokaJapan
  2. 2.Department of Computer ScienceTU DortmundDortmundGermany

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