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The Number of Runs in a String: Improved Analysis of the Linear Upper Bound

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STACS 2006 (STACS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

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Abstract

A run (or a maximal repetition) in a string is an inclusion-maximal periodic segment in a string. Let ρ(n) be the maximal number of runs in a string of length n. It has been shown in [8] that ρ(n)=O(n), the proof was very complicated and the constant coefficient in O(n) has not been given explicitly. We propose a new approach to the analysis of runs based on the properties of subperiods: the periods of periodic parts of the runs. We show that ρ(n) ≤ 5 n. Our proof is inspired by the results of [4], where the role of new periodicity lemmas has been emphasized.

Research supported by the grants 4T11C04425 and CCR-0313219.

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Rytter, W. (2006). The Number of Runs in a String: Improved Analysis of the Linear Upper Bound. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_14

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  • DOI: https://doi.org/10.1007/11672142_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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