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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

Outgoing Edge Integer Array Link Path Link Tree Gapped Repeat 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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