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While skid trails and logging decks generally close rapidly after logging, logging roads may be reopened and persist for decades in the landscape [15].
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Our algorithm sorts n integers in the range {0, 1, 2, …, m−1} in linear space in O(n log log n log log log n) time.
This improves upon the result of Bartal who gave a bound of O log n log log n).
A (mathcal {O}(log n log log n)) pseudo-approximation algorithm was proposed in [13].
random variables and set S n = ∑ j = 1 n X j for n ≥ 1, log x = ln ( x ∨ e ) and log log x = log ( log x ).
This requires adding 2 N Θ + O ( N 3 / 4 log ( N ) log ( log ( N ) ) ) new variables.
A similar convention applies to logarithms, where log2x usually means (log x 2, not log log x.
Kao et al. [ 21] presented a randomized algorithm with running time O(n log n log log n) using O(n log n log log n) experiments.
Our nonconservative sorting algorithm sorts n integers in {0, 1, …, m−1} in time O(n(log log n 2/(log k+log log log n)) using word length k log(m+n), where k≤log n.
Our EREW parallel algorithm sorts n integers in {0, 1, …, m−1} in O((log n 2) time and O(n(log log n 2/log log log n) operations provided log m=Ω((log n 2).
On the other hand, let ε n = n − 1 / 6 ⋅ log n ⋅ log log n.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com