The “Runs” Theorem
نویسندگان
چکیده
منابع مشابه
Beyond the Runs Theorem
In [2], a short and elegant proof was presented showing that a binary word of length n contains at most n − 3 runs. Here we show, using the same technique and a computer search, that the number of runs in a binary word of length n is at most 22 23 n < 0.957n.
متن کاملThe "Runs" Theorem
We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon words. The characterization leads to a proof of the so-called runs conjecture (Kolpakov & Kucherov (FOCS ’99)), which states that the maximum number of runs ρ(n) in a string of length n is less than n. The proof is remarkably simple, considering the numerous endeavors to tackle this problem in the last 15...
متن کاملA Central Limit Theorem for the Number of Success Runs: an Example of Regenerative Processes
Abstract: For each n ≥ 1, let {Xn,j , j ≥ 1} be i.i.d. Bernoulli random variables with P{Xn,1 = 1} = pn = 1 − qn = 1 − P{Xn,1 = 0}, 0 < pn < 1. Define Wn,mn = ∑mn j=1 (Rn,j −an), where Rn,j = inf{k ≥ 0 : Xn,j+k = 0} is the number of success runs starting at j, mn is a sequences of positive integers, and an = pn/qn. We show that, under the condition mnpn → ∞, the central limit theorem Wn,mn σmn ...
متن کاملMaking the DDA Run: Two-Dimensional Ray Traversal Using Runs and Runs of Runs
Iterative algorithms based on runs and runs of runs are presented to calculate the cells of the two–dimensional lattice intersected by a line of real slope and intercept. The technique is applied to the problem of traversing a ray through a two–dimensional grid. Using runs or runs of runs provides a significant improvement in the efficiency of ray traversal for all but very short path lengths w...
متن کاملWhen Short Runs Beat Long Runs
What will yield the best results: doing one run n generations long or doing m runs n/m generations long each? This paper presents a techniqueindependent analysis which answers this question, and has direct applicability to scheduling and restart theory in evolutionary computation and other stochastic methods. The paper then applies this technique to three problem domains in genetic programming....
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2017
ISSN: 0097-5397,1095-7111
DOI: 10.1137/15m1011032