License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.39
URN: urn:nbn:de:0030-drops-57408
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5740/
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Gawrychowski, Pawel ; I, Tomohiro ; Inenaga, Shunsuke ; Köppl, Dominik ; Manea, Florin

Efficiently Finding All Maximal alpha-gapped Repeats

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Abstract

For alpha >=1, an alpha-gapped repeat in a word w is a factor uvu of w such that |uv| <= alpha * |u|; the two occurrences of a factor u in such a repeat are called arms. Such a repeat is called maximal if its arms cannot be extended simultaneously with the same symbol to the right nor to the left. We show that the number of all maximal alpha-gapped repeats occurring in words of length n is upper bounded by 18 * alpha * n, allowing us to construct an algorithm finding all maximal alpha-gapped repeats of a word on an integer alphabet of size n^{O}(1)} in {O}(alpha * n) time. This result is optimal as there are words that have Theta(alpha * n) maximal alpha-gapped repeats. Our techniques can be extended to get comparable results in the case of alpha-gapped palindromes, i.e., factors uvu^{T} with |uv| <= alpha |u|.

BibTeX - Entry

@InProceedings{gawrychowski_et_al:LIPIcs:2016:5740,
  author =	{Pawel Gawrychowski and Tomohiro I and Shunsuke Inenaga and Dominik K{\"o}ppl and Florin Manea},
  title =	{{Efficiently Finding All Maximal alpha-gapped Repeats}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{39:1--39:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5740},
  URN =		{urn:nbn:de:0030-drops-57408},
  doi =		{10.4230/LIPIcs.STACS.2016.39},
  annote =	{Keywords: combinatorics on words, counting algorithms}
}

Keywords: combinatorics on words, counting algorithms
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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