TY - GEN

T1 - Average value of sum of exponents of runs in strings

AU - Kusano, Kazuhiko

AU - Matsubara, Wataru

AU - Ishino, Akira

AU - Shinohara, Ayumi

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:84869106882

SN - 9788001041451

T3 - Proceedings of the Prague Stringology Conference 2008

SP - 185

EP - 192

BT - Proceedings of the Prague Stringology Conference 2008

T2 - Prague Stringology Conference 2008, PSC 2008

Y2 - 1 September 2008 through 3 September 2008

ER -