An asymptotic lower bound for the maximal-number-of-runs function
نویسندگان
چکیده
An asymptotic lower bound for the maxrun function ρ(n) = max {number of runs in string x | all strings x of length n} is presented. More precisely, it is shown that for any ε > 0, (α−ε)n is an asymptotic lower bound, where α = 3 1+ √ 5 ≈ 0.927. A recent construction of an increasing sequence of binary strings “rich in runs” is modified and extended to prove the result.
منابع مشابه
An asymptotic Lower Bound for the Maximal Number of Runs in a String
An asymptotic lower bound for the maxrun function ρ(n) = max {number of runs in string x | all strings x of length n} is presented. More precisely, it is shown that for any ε > 0, (α−ε)n is an asymptotic lower bound, where α = 3 1+ √ 5 ≈ 0.927. A recent construction of an increasing sequence of binary strings “rich in runs” is modified and extended to prove the result.
متن کاملNot So Many Runs in Strings
Since the work of Kolpakov and Kucherov in [5, 6], it is known that ρ(n), the maximal number of runs in a string, is linear in the length n of the string. A lower bound of 3/(1 + √ 5)n ∼ 0.927n has been given by Franek and al. [3, 4], and upper bounds have been recently provided by Rytter, Puglisi and al., and Crochemore and Ilie (1.6n) [8, 7, 1]. However, very few properties are known for the ...
متن کاملMaximal Independent Sets for the Pixel Expansion of Graph Access Structure
Abstract : A visual cryptography scheme based on a given graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper a maximal independent sets of the graph G was ...
متن کاملMAXIMAL INDEPENDENT SETS FOR THE PIXEL EXPANSION OF GRAPH ACCESS STRUCTURE
Given a graph G, a visual cryptography scheme based on the graph G is a method to distribute a secret image among the vertices of G, the participants, so that a subset of participants can recover the secret image if they contain an edge of G, by stacking their shares, otherwise they can obtain no information regarding the secret image. In this paper we apply maximal independent sets of the grap...
متن کاملOn the Maximal Number of Cubic Runs in a String
A run is an inclusion maximal occurrence in a string (as a subinterval) of a factor in which the period repeats at least twice. The maximal number of runs in a string of length n has been thoroughly studied, and is known to be between 0.944n and 1.029n. The proofs are very technical. In this paper we investigate cubic runs, in which the period repeats at least three times. We show the upper bou...
متن کامل