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Understanding Maximal Repetitions in Strings

Authors Maxime Crochemore, Lucian Ilie



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Maxime Crochemore
Lucian Ilie

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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)
https://doi.org/10.4230/LIPIcs.STACS.2008.1344

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.
Keywords
  • Combinatorics on words
  • repetitions in strings
  • runs
  • maximal repetitions
  • maximal periodicities
  • sum of exponents

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