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
Average-Case Analysis of Algorithms and Data Structures.
TL;DR: The authors discusses the analytic methods for average-case analysis of algorithms, with special emphasis on the main algorithms and data structures used for processing non-numerical data, and presents complex asymptotic methods, based upon singularity analysis and saddle point integrals.
Journal ArticleDOI
The de Bruijn multiprocessor network: a versatile parallel processing and sorting network for VLSI
TL;DR: It is shown that the binary de Bruijn multiprocessor network (BDM) can solve a wide variety of classes of problems and is more versatile than the shuffle-exchange and the cube-connected cycles.
Book ChapterDOI
Perfectly secure oblivious RAM without random oracles
TL;DR: In this article, a lower bound on the amount of randomness needed for implementing an information theoretically secure oblivious RAM is proved, without assuming that the CPU has access to a random oracle.
Journal ArticleDOI
Counting networks
TL;DR: Two counting network constructions are given that avoid the sequential bottlenecks inherent to earlier solutions and substantially lower the memory contention, and are provided with experimental evidence that they outperform conventional synchronization techniques under a variety of circumstances.
Journal ArticleDOI
A taxonomy of parallel sorting
TL;DR: This paper analyzes the evolution of research on parallel sorting, from the earliest sorting networks to the shared memory algorithms and the VLSI sorters, and proposes a taxonomy of parallel sorting that includes a broad range of array and file sorting algorithms.
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.