Locating maximal approximate runs in a string
نویسندگان
چکیده
منابع مشابه
On 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 کاملOn the maximal number of highly periodic runs in a string
A run is a maximal occurrence of a repetition v with a period p such that 2p ≤ |v|. The maximal number of runs in a string of length n was studied by several authors and it is known to be between 0.944n and 1.029n. We investigate highly periodic runs, in which the shortest period p satisfies 3p ≤ |v|. We show the upper bound 0.5n on the maximal number of such runs in a string of length n and co...
متن کاملAn 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 کامل[hal-00742081, v1] On the Maximal Sum of Exponents of Runs in a String
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 4.1n is better than the best previously known proven bound of 5.6n by Crochemore & Ilie (2008). The lower bound of...
متن کاملHow many runs can a string contain?
Given a string x = x[1..n], a repetition of period p in x is a substring ur = x[i+1..i+rp], p = |u|, r ≥ 2, where neither u = x[i+1..i+p] nor x[i+1..i+(r+1)p+1] is a repetition. The maximum number of repetitions in any string x is well known to be Θ(n log n). A run or maximal periodicity of period p in x is a substring urt = x[i+1..i+rp+ |t|] of x, where ur is a repetition, t a proper prefix of...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2017
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2017.07.021