Journal ArticleDOI
Parallel sorting in two-dimensional VLSI models of computation
Isaac D. Scherson,Sandeep Sen +1 more
TLDR
The gradual refinement of a general approach to two-dimensional sorting, the shear-sort algorithm, to more sophisticated and specialized sorting algorithms on mesh-connected computers is described.Abstract:
The gradual refinement of a general approach to two-dimensional sorting, the shear-sort algorithm, to more sophisticated and specialized sorting algorithms on mesh-connected computers is described. The analysis of the shear-sort algorithm gives rise to a novel perspective of two-dimensional sorting, which seems to be a very powerful tool for developing efficient algorithms. The same methods can be extended for sorting in higher dimensions, for example, in the three-dimensional mesh. The concept of clean and dirty rows can be modified to clean and dirty planes (or hyperplanes for dimensions greater than three). Although only two schemes (purely recursive and iterative) are explicitly described, the reader may construct his own algorithm using similar technique and slight modifications. Designing an O(n) algorithm for sorting on a mesh becomes much simpler using the techniques developed. >read more
Citations
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Journal ArticleDOI
Packet Routing in Fixed-Connection Networks
TL;DR: This work focuses on (partial) permutation, k-relation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results.
Proceedings ArticleDOI
Randomized Shellsort: a simple oblivious sorting algorithm
TL;DR: This algorithm is a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and succeeds in sorting any given input permutation with very high probability.
Proceedings ArticleDOI
An optimal sorting algorithm on reconfigurable mesh
Ju-wook Jang,Viktor K. Prasanna +1 more
TL;DR: The presented algorithm satisfies the AT/Sup 2/ lower bound of Omega (n/sup 2/) for sorting n numbers in the word model of VLSI for optimal sorting on the reconfigurable mesh.
Proceedings ArticleDOI
Kerrighed and data parallelism: cluster computing on single system image operating systems
Christine Morin,Renaud Lottiaux,Geoffroy Vallée,P. Gallard,David Margery,J.-Y. Berthou,Isaac D. Scherson +6 more
TL;DR: It is shown that ShearSort is remarkably well suited for the architecture/system pair as is the ever so popular and important two-dimensional fast Fourier transform.
Proceedings Article
The Distance Bound for Sorting on Mesh-Connected Processor Arrays Is Tight (Preliminary Report)
Abstract: In this paper, We consider the problem of sorting n2 numbers, initially distributed randomly in an n × n mesh-connected processor array with one element per processor. We show a lower bound, based on distance arguments, of 4n routing steps on mesh-connected processors operating in an SIMD mode with no wraparounds in rows or columns, We present an algorithm using a novel approach, which is optimal upto the conslant of the leading term, and hence, succeed in proving the tightness of the lower bound based on distance. Keeping in mind the practical difficulties in implementation of this algorithm, we also present an extremely practical O(n) algorithm amenable for VLSI implementation and for existing mesh- connected computers. All the results in this paper were derived by using a new method of analysis inspired by the discovery of shear-sort or row-column sort.
References
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Journal ArticleDOI
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.
Proceedings ArticleDOI
An 0(n log n) sorting network
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.
Journal ArticleDOI
Sorting on a mesh-connected parallel computer
C. D. Thompson,Hsiang-Tsung Kung +1 more
TL;DR: Two algorithms are presented for sorting n2 elements on an n × n mesh-connected processor array that require O (n) routing and comparison steps and are shown to be optimal in time within small constant factors.
Journal ArticleDOI
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.
Book
Parallel merge sort
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.