An optimal and processor efficient parallel sorting algorithm on a linear array with a reconfigurable pipelined bus system

Optical interconnections attract many engineers and scientists’ attention due to their potential for gigahertz transfer rates and concurrent access to the bus in a pipelined fashion. These unique characteristics of optical interconnections give us the opportunity to reconsider traditional algorithms designed for ideal parallel computing models, such as PRAMs. Since the PRAM model is far from practice, not all algorithms designed on this model can be implemented on a realistic parallel computing system. From this point of view, we study Cole’s pipelined merge sort [Cole R. Parallel merge sort. SIAM J Comput 1988;14:770–85] on the CREW PRAM and extend it in an innovative way to an optical interconnection model, the LARPBS (Linear Array with Reconfigurable Pipelined Bus System) model [Pan Y, Li K. Linear array with a reconfigurable pipelined bus system—concepts and applications. J Inform Sci 1998;106;237–58]. Although Cole’s algorithm is optimal, communication details have not been provided due to the fact that it is designed for a PRAM. We close this gap in our sorting algorithm on the LARPBS model and obtain an O(log N)-time optimal sorting algorithm using O(N) processors. This is a substantial improvement over the previous best sorting algorithm on the LARPBS model that runs in O(log N log log N) worst-case time using N processors [Datta A, Soundaralakshmi S, Owens R. Fast sorting algorithms on a linear array with a reconfigurable pipelined bus system. IEEE Trans Parallel Distribut Syst 2002;13(3):212–22]. Our solution allows efficiently assign and reuse processors. We also discover two new properties of Cole’s sorting algorithm that are presented as lemmas in this paper.     

排序算法与全排列生成算法研究

引入排序计算树和排列枚举树的概念,研究某些排序算法和全排列生成算法之间的关系,由插入排序算法直接导出了一个全排列生成算法,也由一个全排列生成算法导出了一个排序算法.     

如何提高编程效率

本文主要通过slit算法的功能模块划分，在实现该运算中特别注意内存空间的分配与排序算法的选择，通过分析排序算法的优劣来选择适当的排序算法。文章最后总结该过程，得到如何提高编程效率的心得。     

Simplified odd-even sort using multiple shift-register loops

By using anN-loop shift-register structure called a uniform ladder,N records can be sorted by a simplified adaptation of the odd-even transposition-sort algorithm to finish in (N + 1)/2 loop times (periods) using (N – 1) comparators. The sorting can be overlapped with input/output; the percentage of unoverlapped sorting times is less than 20% of the total time with a single ladder, less than 6% using two ladders, and is zero with a sufficient number of ladders.Presented at the Second International Magnetic Bubble Conference, Eindhoven, The Netherlands, August 1976.     

A faster algorithm for sorting on mesh-connected computers with multiple broadcasting using fewer processors

This paper presents an efficient parallel algorithm for sorting N data items on two-dimensional mesh connected-computers with multiple broadcasting (2-MCCMB). The algorithm uses N × N ^2/3 processors and takes 0(N ^1/3) time, whereas the previous algorithm by Chung-Horng Lung [3] uses N × N processors and takes 0(N ^l/2) time on 2-MCCMB.     

A new external sorting algorithm with no additional disk space

This paper is concerned with an external sorting algorithm with no additional disk space. The proposed algorithm is a hybrid one that uses Quicksort and special merging process in two distinct phases. The algorithm excels in sorting a huge file, which is many times larger than the available memory of the computer. This algorithm creates no extra backup file for manipulating huge records. For this, the algorithm saves huge disk space, which is needed to hold the large file. Also our algorithm switches to special merging process after the first phase that uses Quicksort. This reduces the time complexity and makes the algorithm faster.     

基于Quick Sorting的快速分页排序算法

提出了分页排序的概念和基于Quick Sorting的快速分页排序算法(Quick Page Sorting)以及基于Hinl缓存机制的算法实现技术。实验表明,在数万至数百万数据总量情况下,Quick Pagc Soring的速度比Quick Sorting快10倍左右,大大提高了应用系统的响应速度。     

针对任意分布数据的高效分档混合排序算法

针对任意分布数据的排序问题,在把对文献[7][8][9]等分档排序算法的改进与该算法在程序语言中的实现技术的改进相结合的基础上,提出了一种新的针对任意分布数据的高效分“档”排序算法,并通过把它与最近排序方面的工作进行比较说明了它的优越性。     

不改变数据位置的排序算法及动态演示

实际应用中经常遇到要求不改变原始数据的顺序而按关键字的大小对数据进行排序的情况,原有的一些经典排序算法不能直接用于解决该类问题。经过对选择排序算法进行研究,给出基于选择思想的不改变数据位置而对数据进行排序的算法,并利用C#语言编程对该算法的实现过程进行动态演示。     

An efficient external sorting with minimal space requirement

An efficient external sorting algorithm with minimal space requirement is presented in this article. The average number of passes over the data is approximately 1 +Ln(N + 1)/4B, whereN is the number of records in the file to be sorted, andB is the buffer size. The external storage requirement is only the file itself, no additional disk space is required. The internal storage requirement is four buffers: two for input, and two for output. The buffer size can be adjusted to the available memory space. A stack of size log₂ N is also required.This work was partially supported by a fellowship and grant from Western Michigan University.     

一种新型快速的排序算法

提出了一种简单快速的新的排序算法，并对其性能与快速排序算法的性能进行了实验比较。     

B-快速排序算法的研究与应用

描述了B-快速排序的基本思想，提出了正确的实现算法，然后给出了两种结构形式的、用C 实现的程序源代码，最后介绍了它在并行程序监测分析工具软件中的应用。     

基于存储结构的汉字分组排序及其复杂度分析

自从计算机被用来进行大规模的数据处理,数据序列的排序问题便一直成为研究的热点,汉语言本身所具有的特点,使得汉字符串的排序问题成为中文信息处理领域中备受关注的问题,提出了一种汉字符串的快速分组排序算法,算法复杂度仅为O(n)。     

Sorting in constant number of row and column phases on a mesh

An algorithm for sorting on a mesh by alternately transforming the rows and columns is presented. The algorithm runs in a constant number of row- and column-transformation phases (sixteen phases), an improvement over the previous best upper bound ofO(log logm) phases,m being the number of rows in the mesh. A corresponding lower bound of five phases is also shown.This research was supported by the National Science Foundation under Grant DCR-84-51396, and by IBM Corporation under Grant D8400622.     

Sorting and Searching in Faulty Memories

In this paper we investigate the design and analysis of algorithms resilient to memory faults. We focus on algorithms that, despite the corruption of some memory values during their execution, are nevertheless able to produce a correct output at least on the set of uncorrupted values. In this framework, we consider two fundamental problems: sorting and searching. In particular, we prove that any O(nlog n) comparison-based sorting algorithm can tolerate the corruption of at most O((nlog n)^1/2) keys. Furthermore, we present one comparison-based sorting algorithm with optimal space and running time that is resilient to O((nlog n)^1/3) memory faults. We also prove polylogarithmic lower and upper bounds on resilient searching. This work has been partially supported by the Sixth Framework Programme of the EU under Contract Number 507613 (Network of Excellence “EuroNGI: Designing and Engineering of the Next Generation Internet”) and by MIUR, the Italian Ministry of Education, University and Research, under Project ALGO-NEXT (“Algorithms for the Next Generation Internet and Web: Methodologies, Design and Experiments”). A preliminary version of this work was presented at the 36th ACM Symposium on Theory of Computing (STOC’04) .     

一种新的分"档"统计插入排序算法

提出了一种谓之数据代码转换,分“档”统计,迁移插入的新排序方法,给出了该排序算法的描述,时间复杂度分析用Ｃ语言编写程序进行算法比较的实验结果,算法分析和实验结果都表明：在待排序数据均匀分布的情况下,分“档”统计插入排序方法的时间复杂度为Ｏ（Ｎ）,并且排序速度明显优于快速排序,分段快速排序,按位段分块排序等算法。     

基于特定范围的关键字的快速排序算法

本文给出了一种对关键字在特定范围内的数据记录不用进行数据的比较交换的快速排序算法、算法思想、算法描述、时间复杂度及空间复杂度分析,并用C＋＋语言编写程序进行算法比较。结果表明：在关键字范围远远小于记录数的情况下,此算法的时间复杂度仅为O（n）,并且明显优于其他排序算法。     

A PRACTICAL ALGORITHM for INTEGER SORTING INTEGER SORTING ON A MESH-CONNECTED COMPUTER*

This paper presents count-sort, a parallel algorithm for mesh-connected computers to sort integers where the range of inputs is known. A straightforward counting technique that has not been implemented previously in parallel sorting algorithms is presented. On a mesh-connected computer with N×N processors we are able to sort N integers in the range 1 sN in timewhere cN is very small. For practical values of N, the algorithm is extremely fast. Further, it is possible to expand the range by a factor k to 1 N so that the slowdown is less than k.

We produce two implementations of count-sort on the SIMD MasPar MP-I with 8192 processors. The first sorts 8-bit integers, one per processor, significantly faster than the manufacturer's current library routine for sorting 8-bit integers. The second implementation is a fast version that sorts several elements per processor.     

不改变数据位置的排序算法及动态演示

实际应用中经常遇到要求不改变原始数据的顺序而按关键字的大小对数据进行排序的情况,原有的一些经典排序算法不能直接用于解决该类问题。经过对选择排序算法进行研究,给出基于选择思想的不改变数据位置而对数据进行排序的算法,并利用C#语言编程对该算法的实现过程进行动态演示。     

程序设计中常用的排序算法

针对程序设计中常出现的排序问题，介绍了六种常用的排序算法：插入排序、希尔排序、堆排序、归并排序、冒泡排序、快速排序，以及每种排序所需的时间复杂度，当对大量的数据排序时，以选择适应的算法，提高程序的执行速度。