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Bitonic sorter

About: Bitonic sorter is a research topic. Over the lifetime, 446 publications have been published within this topic receiving 12419 citations.


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Proceedings ArticleDOI
30 Apr 1968
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.
Abstract: 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. A major problem in the design of such a computing system is the connecting together of the various parts of the system (the I/O devices, memories, processing units, etc.) in such a way that all the required data transfers can be accommodated. One common scheme is a high-speed bus which is time-shared by the various parts; speed of available hardware limits this scheme. Another scheme is a cross-bar switch or matrix; limiting factors here are the amount of hardware (an m × n matrix requires m × n cross-points) and the fan-in and fan-out of the hardware.

2,553 citations

Proceedings ArticleDOI
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.
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.

683 citations

Journal ArticleDOI
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.
Abstract: Two algorithms are presented for sorting n2 elements on an n × n mesh-connected processor array that require O (n) routing and comparison steps. The best previous algoritmhm takes time O(n log n). The algorithms of this paper are shown to be optimal in time within small constant factors. Extensions to higher-dimensional arrays are also given.

489 citations

DissertationDOI
01 Jan 1999
TL;DR: This thesis presents efficient algorithms for internal and external parallel sorting and remote data update and examines a number of related algorithms for text compression, differencing and incremental backup.
Abstract: This thesis presents efficient algorithms for internal and external parallel sorting and remote data update. The sorting algorithms approach the problem by concentrating first on highly efficient but incorrect algorithms followed by a cleanup phase that completes the sort. The remote data update algorithm, rsync, operates by exchanging block signature information followed by a simple hash search algorithm for block matching at arbitrary byte boundaries. The last chapter of the thesis examines a number of related algorithms for text compression, differencing and incremental backup.

431 citations

Proceedings ArticleDOI
01 Jun 1991
TL;DR: A fast sorting algorithm for the Connection Machine Supercomputer model CM-2 is developed and it is shown that any U(lg n)-depth family of sorting networks can be used to sort n numbers in U( lg n) time in the bounded-degree fixed interconnection network domain.
Abstract: Sorting is arguably the most studied problem in computer science, both because it is used as a substep in many applications and because it is a simple, combinatorial problem with many interesting and diverse solutions. Sorting is also an important benchmark for parallel supercomputers. It requires significant communication bandwidth among processors, unlike many other supercomputer benchmarks, and the most efficient sorting algorithms communicate data in irregular patterns. Parallel algorithms for sorting have been studied since at least the 1960’s. An early advance in parallel sorting came in 1968 when Batcher discovered the elegant U(lg2 n)-depth bitonic sorting network [3]. For certain families of fixed interconnection networks, such as the hypercube and shuffle-exchange, Batcher’s bitonic sorting technique provides a parallel algorithm for sorting n numbers in U(lg2 n) time with n processors. The question of existence of a o(lg2 n)-depth sorting network remained open until 1983, when Ajtai, Komlos, and Szemeredi [1] provided an optimal U(lg n)-depth sorting network, but unfortunately, their construction leads to larger networks than those given by bitonic sort for all “practical” values of n. Leighton [15] has shown that any U(lg n)-depth family of sorting networks can be used to sort n numbers in U(lg n) time in the bounded-degree fixed interconnection network domain. Not surprisingly, the optimal U(lg n)-time fixed interconnection sorting networks implied by the AKS construction are also impractical. In 1983, Reif and Valiant proposed a more practical O(lg n)-time randomized algorithm for sorting [19], called flashsort. Many other parallel sorting algorithms have been proposed in the literature, including parallel versions of radix sort and quicksort [5], a variant of quicksort called hyperquicksort [23], smoothsort [18], column sort [15], Nassimi and Sahni’s sort [17], and parallel merge sort [6]. This paper reports the findings of a project undertaken at Thinking Machines Corporation to develop a fast sorting algorithm for the Connection Machine Supercomputer model CM-2. The primary goals of this project were:

362 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20213
20207
20193
20185
20179
20168