Finding Maximal Repetitions in a Word in Linear Time

1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : A repetition in a word $w$ is a subword with the period of at most half of the subword length. We study maximal repetitions occurring in $w$, that is those for which any extended subword of $w$ has a bigger period. The set of such repetitions represents in a compact way all repetitions in $w$. We first prove a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length $n$ is bounded by a linear function in $n$. This implies, in particular, that there is only a linear number of maximal repetitions in a word. This allows us to construct a linear-time algorithm for finding all maximal repetitions. Some consequences and applications of these results are discussed, as well as related works.
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Conference papers
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https://hal.inria.fr/inria-00098853
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Submitted on : Tuesday, September 26, 2006 - 8:39:18 AM
Last modification on : Friday, February 4, 2022 - 3:31:07 AM

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• HAL Id : inria-00098853, version 1

Citation

Roman Kolpakov, Gregory Kucherov. Finding Maximal Repetitions in a Word in Linear Time. 1999 Symposium on Foundations of Computer Science - FOCS'99, IEEE Computer Society, 1999, New-York, USA, pp.596--604. ⟨inria-00098853⟩

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