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DOI: 10.4230/LIPIcs.STACS.2008.1344

Understanding Maximal Repetitions in Strings

Authors: Maxime Crochemore and Lucian Ilie

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract

The cornerstone of any algorithm computing all repetitions in a string of length $n$ in ${mathcal O(n)$ time is the fact that the number of runs (or maximal repetitions) is ${mathcal O(n)$. We give a simple proof of this result. As a consequence of our approach, the stronger result concerning the linearity of the sum of exponents of all runs follows easily.

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Maxime Crochemore and Lucian Ilie. Understanding Maximal Repetitions in Strings. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 11-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{crochemore_et_al:LIPIcs.STACS.2008.1344,
  author =	{Crochemore, Maxime and Ilie, Lucian},
  title =	{{Understanding Maximal Repetitions in Strings}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{11--16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1344},
  URN =		{urn:nbn:de:0030-drops-13442},
  doi =		{10.4230/LIPIcs.STACS.2008.1344},
  annote =	{Keywords: Combinatorics on words, repetitions in strings, runs, maximal repetitions, maximal periodicities, sum of exponents}
}

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Understanding Maximal Repetitions in Strings

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