Average value of sum of exponents of runs in strings

Kazuhiko Kusano, Wataru Matsubara, Akira Ishino, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

A substring w[i.j] in w is called a repetition of period p if s[k] = s[k + p] for any i ≤ k ≤ j - p. Especially, a maximal repetition, which cannot be extended neither to left nor to right, is called a run. The ratio of the length of the run to its period, i.e. j-i+1/p, is called an exponent. The sum of exponents of runs in a string is of interest. The maximal value of the sum is still unknown, and the current upper bound is 2.9n given by Crochemore and Ilie, where n is the length of a string. In this paper we show a closed formula which exactly expresses the average value of it for any n and any alphabet size, and the limit of this value per unit length as n approaches infinity. For binary strings, the limit value is approximately 1.13103.

Original languageEnglish
Title of host publicationProceedings of the Prague Stringology Conference 2008
Pages185-192
Number of pages8
Publication statusPublished - 2008 Dec 1
EventPrague Stringology Conference 2008, PSC 2008 - Prague, Czech Republic
Duration: 2008 Sep 12008 Sep 3

Publication series

NameProceedings of the Prague Stringology Conference 2008

Other

OtherPrague Stringology Conference 2008, PSC 2008
CountryCzech Republic
CityPrague
Period08/9/108/9/3

ASJC Scopus subject areas

  • Mathematics(all)

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  • Cite this

    Kusano, K., Matsubara, W., Ishino, A., & Shinohara, A. (2008). Average value of sum of exponents of runs in strings. In Proceedings of the Prague Stringology Conference 2008 (pp. 185-192). (Proceedings of the Prague Stringology Conference 2008).