Maximal Repetitions in Words or How to Find all Squares in Linear Time
Identifieur interne : 00B631 ( Main/Exploration ); précédent : 00B630; suivant : 00B632Maximal Repetitions in Words or How to Find all Squares in Linear Time
Auteurs : Roman Kolpakov [France] ; Gregory Kucherov [France]Source :
Descripteurs français
Abstract
A (fractional) 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 count the exact number of maximal repetitions in Fibonacci words. Then we prove our main result asserting that the maximal number of such repetitions in general words (on arbitrary alphabet) is linear in the length. We then show how this result implies a linear-time algorithm for finding all maximal repetitions.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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motifs</term><term>répétitions</term><term>word combinatorics</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">A (fractional) 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 count the exact number of maximal repetitions in Fibonacci words. Then we prove our main result asserting that the maximal number of such repetitions in general words (on arbitrary alphabet) is linear in the length. We then show how this result implies a linear-time algorithm for finding all maximal repetitions.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Kolpakov, Roman" sort="Kolpakov, Roman" uniqKey="Kolpakov R" first="Roman" last="Kolpakov">Roman Kolpakov</name></region><name sortKey="Kucherov, Gregory" sort="Kucherov, Gregory" uniqKey="Kucherov G" first="Gregory" last="Kucherov">Gregory Kucherov</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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