线性数列排序网络模型的计算复杂度

T. Martyniuk, O. I. Chernyak, B. Krukivskyi, Mohamed Salem Nasser Mohamed
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引用次数: 0

摘要

在为现代计算开发先进的软件和硬件的过程中,兴趣在于改进信息的联想处理方法,如排序和选择程序。这保证了在数据数组中实现对所需信息的有效搜索。对大量信息进行并行非处理的需要需要对联想记忆进行适当的组织,以及开发和使用透视技术设备。排序是解决经济问题、管理数据库、计算机网络中IP地址排序、处理信号和图像(如非线性中值图像滤波)等应用领域的重要过程。对已知排序方法的分析表明,考虑到排序网络的硬件实现,最有效的并行排序方法是成对交换。同时,任何排序方法的硬件实现的并行度直接取决于在每个视图中并行工作的比较方案的数量。对于两两交换方法,并行度由值[n/2]决定,其中n为输入数值的个数或输入线性数数组的维数。本文分析了用“带”形和“环”形数字数组元素间的链路拓扑对交换的方法来实现排序算法的方法。例如,描述了使用成对交换方法的并行排序算法。仿真是在高级c++语言中完成的。对所得到的建模统计结果和图形结果进行了分析。图形化建模结果分析表明,排序循环数与输入数组的维数n之间存在O(n)形式的依赖关系。由于排序过程中结构和连接的规律性,这证实了在排序网络上通过配对交换实现排序的硬件实现的有效性。能够统计地确定数字数组给定维数的排序循环次数,以及相应的比较和换位次数,极大地扩展了以排序网络的形式通过硬件改进已知和创建线性数组元素同步排序的新方法的可能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
COMPUTATIONAL COMPLEXITY OF THE NETWORK MODEL OF SORTING OF A LINEAR NUMBER ARRAY
In the development of advanced software and hardware for modern computing, the interest is the improvement of methods of associative processing of information such as procedures of sorting and selection. That ensures the realization of effective search for the required information in the data arrays. The need for parallel non-processing of large amounts of information entails the appropriate organization of associative memory, as well as the development and using of perspective technical devices. The sorting is important procedure in such application areas as solving economic problems, managing databases, sorting of IP addresses in computer networks, processing signals and images (for example, in nonlinear median image filtering). The analysis of known sorting methods have shown that the most effective method of parallel sorting, taking into account its hardware implementation by the sorting network, is the pairwise exchange. At the same time, the degree of parallelism of any sorting method for its hardware implementation directly depends on the number of comparison schemes that work in parallel in each view. For a pairwise exchange method, the degree of parallelism is determined by the value ]n/2[, where n is the number of input numerical values ​​or the dimension of the input linear number array. In this article methods of implementing of the sorting algorithm by the method of pairwise exchange with the link topology between elements of the number array in the form of "tape" and "ring" are analyzed. For example, the parallel sorting algorithm using the pairwise exchange method is described. The simulation at a high-level C ++ language is done. The obtained statistical and graphic results of modeling are analyzed. The analysis of graphical modeling results shows the dependence of the form O(n) between the number of sort cycles and the dimensionality n of the input array. That confirms the effectiveness of the hardware implementation of sorting by pairwise exchange on the sorting network due to the regularity of the structure and connections in the sorting process. The ability to statistically determine not only the number of sorting cycles with a given dimension of  the number array, but also the corresponding number of comparisons and transposition greatly extends the possibilities of improving the known and creating new ways of synchronous sorting of elements of a linear array by hardware in the form of a sorting network.
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