Proceedings ArticleDOI
An 0(n log n) sorting network
Miklós Ajtai,János Komlós,Endre Szemerédi +2 more
- pp 1-9
Reads0
Chats0
TLDR
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.Abstract:
The purpose of this paper is to describe a sorting network of size 0(n log n) and depth 0(log n). A natural way of sorting is through consecutive halvings: determine the upper and lower halves of the set, proceed similarly within the halves, and so on. Unfortunately, while one can halve a set using only 0(n) comparisons, this cannot be done in less than log n (parallel) time, and it is known that a halving network needs (½)n log n comparisons. It is possible, however, to construct a network of 0(n) comparisons which halves in constant time with high accuracy. This procedure (e-halving) and a derived procedure (e-nearsort) are described below, and our sorting network will be centered around these elementary steps.read more
Citations
More filters
Proceedings ArticleDOI
Noncryptographic selection protocols
TL;DR: New selection protocols in the full information model are presented, and new negative results are presented when there are (1+/spl delta/)n/2 good players, and it is shown that every leader election protocol has success probability O.
Proceedings ArticleDOI
GPU-ABiSort: optimal parallel sorting on stream architectures
A. Greb,Gabriel Zachmann +1 more
TL;DR: This paper presents a novel approach for parallel sorting on stream processing architectures based on adaptive bitonic sorting that achieves the optimal time complexity O((n log n)/p) and presents an implementation on modern programmable graphics hardware (GPUs).
Journal ArticleDOI
Extended formulations in combinatorial optimization
TL;DR: This survey presents compact extended formulations for several graph problems involving cuts, trees, cycles and matchings, and for the mixing set, and presents the proof of Fiorini, Massar, Pokutta, Tiwary and de Wolf of an exponential lower bound for the cut polytope.
Journal ArticleDOI
Efficient parallel convex hull algorithms
Russ Miller,Quentin F. Stout +1 more
TL;DR: In this article, a parallel algorithm for finding the extreme points of the convex hull of a set of planar points using a hypercube, pyramid, tree, mesh-of-trees, mesh with reconfigurable bus, exclusive-read-exclusive-write parallel random access machine (EREW PRAM), and modified AKS network is presented.
Proceedings ArticleDOI
An optimal parallel algorithm for integer sorting
TL;DR: This work gives a new parallel algorithm for integer sorting where the integer keys are restricted to at most polynomial magnitude and is the first known where the product of the time and processor bounds are bounded by a linear function of the input size.
References
More filters
Proceedings ArticleDOI
Sorting networks and their applications
TL;DR: To achieve high throughput rates today's computers perform several operations simultaneously; not only are I/O operations performed concurrently with computing, but also, in multiprocessors, several computing operations are done concurrently.
Journal ArticleDOI
Space bounds for a game on graphs
TL;DR: It is shown that for each graph withn vertices and maximum in-degreed, there is a pebbling strategy which requires at mostc(d) n/logn pebbles, and this bound is tight to within a constant factor.
Proceedings ArticleDOI
Explicit constructions of linear size superconcentrators
Ofer Gabber,Zvi Galil +1 more
TL;DR: An explicit construction of an infinite family of N-superconcentrators of density 44 of the most economical previously known explicit graphs of this type is presented.
Proceedings ArticleDOI
On non-linear lower bounds in computational complexity
TL;DR: It is shown that the graph of any algorithm for any one of a number of arithmetic problems (e.g. polynomial multiplication, discrete Fourier transforms, matrix multiplication) must have properties closely related to concentration networks.