Improved upper bounds on shellsort
Janet Incerpi,Robert Sedgewick +1 more
- 07 Nov 1983
- pp 48-55
TL;DR: The running time of Shellsort, with the number of passes restricted to O(log N), was thought for some time to be Θ(N3/2), but a different approach is used to achieve O(N1+4/√2lgN).
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Abstract: The running time of Shellsort, with the number of passes restricted to O(log N), was thought for some time to be Θ(N3/2), due to general results of Pratt Sedgewick recently gave an O(N4/3) bound, but extensions of his method to provide better bounds seem to require new results on a classical problem in number theory In this paper, we use a different approach to achieve O(N1+4/√2lgN)
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Citations
Parallel merge sort
TL;DR: A parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time; the constant in the running time is small.
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Parallel merge sort
Richard Cole
- 09 Sep 2011
TL;DR: In this paper, a parallel implementation of merge sort on a CREW PRAM that uses n processors and O(logn) time is given, and the constant in the running time is small.
Zig-zag sort: a simple deterministic data-oblivious sorting algorithm running in O(n log n) time
Michael T. Goodrich
- 31 May 2014
TL;DR: Zig-zag Sort is a deterministic data-oblivious deterministic sorting algorithm running in O(n log n) time that is arguably simpler than previously known algorithms with similar properties, which are based on the AKS sorting network.
The Frobenius Problem
Ravi Kannan
- 19 Dec 1989
TL;DR: The proof of the structural theorem relies on some recent developments in the Geometry of Numbers and draws on the notion of “width” and covering radius introduced in Kannan and Lovasz, a theorem of Hastad bounding the width of lattice-point-free convex bodies and the techniques to study the shapes of a polyhedron obtained by translating each facet parallel to itself.
41
The Frobenius Problem in a Free Monoid
Jui-Yi Kao,Jeffrey Shallit,Zhi Xu +2 more
- 01 Jan 2008
TL;DR: Novel generalizations of the Frobenius problem to the noncommutative setting of a free monoid are considered and exponential or subexponential behavior for several analogues of $g$ is shown, with the precise bound depending on the particular measure chosen.
References
An 0(n log n) sorting network
Miklós Ajtai,János Komlós,Endre Szemerédi +2 more
- 01 Dec 1983
TL;DR: A sorting network of size 0(n log n) and depth 0(log n) is described, and a derived procedure (&egr;-nearsort) are described below, and the sorting network will be centered around these elementary steps.
752
Tight Bounds on the Complexity of Parallel Sorting
TL;DR: Tight upper and lower bounds are proved on the number of processors, information transfer, wire area, and time needed to sort N numbers in a bounded-degree fixed-connection network.
471
Tight bounds on the complexity of parallel sorting
Tom Leighton
- 01 Dec 1984
TL;DR: Tight upper and lower bounds are proved on the number of processors, information transfer, wire area, and time needed to sort N numbers in a bounded-degree fixed-connection network.
239
A high-speed sorting procedure
TL;DR: It is highly desirable to have a method with the speed characteristics of the merging by pairs and the space characteristics of sifting, if such a method were available, to sort twice as many items at one time in the machine and still do it at a reasonably high speed.
221
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