A faster algorithm for computing maximal α-gapped repeats in a string

Yuka Tanimura, Yuta Fujishige, Tomohiro I, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda

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

12 Citations (Scopus)

Abstract

A string x = uvu with both u, v being non-empty is called a gapped repeat with period p = |uv|, and is denoted by pair (x, p). If p ≤ α(|x| − p) with α > 1, then (x, p) is called an α-gapped repeat. An occurrence [i, i+|x|−1] of an α-gapped repeat (x, p) in a string w is called a maximal α-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 α-gapped repeats in the string can be computed in O(α2n+occ) time, where occ is the number of occurrences. In this paper, we propose a faster O(αn + occ)-time algorithm to solve this problem, improving the result of Kolpakov et al. by a factor of α.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings
EditorsSimon J. Puglisi, Costas S. Iliopoulos, Emine Yilmaz
PublisherSpringer Verlag
Pages124-136
Number of pages13
ISBN (Print)9783319238258
DOIs
Publication statusPublished - 2015
Event22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015 - London, United Kingdom
Duration: Sep 1 2015Sep 4 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9309
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other22nd International Symposium on String Processing and Information Retrieval, SPIRE 2015
CountryUnited Kingdom
CityLondon
Period9/1/159/4/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Tanimura, Y., Fujishige, Y., I, T., Inenaga, S., Bannai, H., & Takeda, M. (2015). A faster algorithm for computing maximal α-gapped repeats in a string. In S. J. Puglisi, C. S. Iliopoulos, & E. Yilmaz (Eds.), String Processing and Information Retrieval - 22nd International Symposium, SPIRE 2015, Proceedings (pp. 124-136). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9309). Springer Verlag. https://doi.org/10.1007/978-3-319-23826-5_13