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Conference Papers Year : 1999

Finding Maximal Repetitions in a Word in Linear Time

Roman Kolpakov
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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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Dates and versions

inria-00098853 , version 1 (26-09-2006)


  • HAL Id : inria-00098853 , version 1


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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