Abstract
A run is an inclusion maximal occurrence in a string (as a subinterval) of a repetition v with a period p such that 2p ≤ |v|. The exponent of a run is defined as |v|/p and is ≥ 2. We show new bounds on the maximal sum of exponents of runs in a string of length n. Our upper bound of 4.1 n is better than the best previously known proven bound of 5.6 n by Crochemore & Ilie (2008). The lower bound of 2.035 n, obtained using a family of binary words, contradicts the conjecture of Kolpakov & Kucherov (1999) that the maximal sum of exponents of runs in a string of length n is smaller than 2n. © 2011 Springer-Verlag.
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CITATION STYLE
Crochemore, M., Kubica, M., Radoszewski, J., Rytter, W., & Waleń, T. (2011). On the maximal sum of exponents of runsin a string. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6460 LNCS, pp. 10–19). https://doi.org/10.1007/978-3-642-19222-7_2
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