一种基于n-Sorters的增强型多路排序网络
An Enhanced Multiway Sorting Network Based on n-Sorters
摘要：
基于归并的排序网络是一类重要的排序网络。大多数归并排序网络是基于2路或多路归并算法，使用2-排序器作为基本构建块。一种替代方案是使用n-排序器而不是2-排序器作为基本构建块，以便大大减少排序器的数量以及延迟。在改进Leighton列排序算法的基础上，提出了一种以n个排序器为基本构件的n路归并算法SS-Mk。在这项工作中，我们首先提出了一个新的多路合并算法与n-sorters作为基本构建块，合并n个排序列表的m个值，每个在1 + ceil（m/2）阶段（n <= m）。基于我们的合并算法，我们还提出了一个排序算法，它需要O（N log 2 N）的基本排序器排序N个输入。虽然我们的排序算法的渐近复杂性（在所需的排序器数量方面）与SS-Mk相同，但对于宽范围的N，我们的算法需要比SS-Mk更少的排序器。最后，我们考虑一个二进制排序网络，其中的基本排序器是在阈值逻辑和规模与输入的数量呈线性关系，并比较所需的门的数量方面的复杂性。对于宽范围的N，我们的算法需要更少的门比SS-Mk。
英文摘要：
Merging-based sorting networks are an important family of sorting networks. Most merge sorting networks are based on 2-way or multi-way merging algorithms using 2-sorters as basic building blocks. An alternative is to use n-sorters, instead of 2-sorters, as the basic building blocks so as to greatly reduce the number of sorters as well as the latency. Based on a modified Leighton's columnsort algorithm, an n-way merging algorithm, referred to as SS-Mk, that uses n-sorters as basic building blocks was proposed. In this work, we first propose a new multiway merging algorithm with n-sorters as basic building blocks that merges n sorted lists of m values each in 1 + ceil(m/2) stages (n <= m). Based on our merging algorithm, we also propose a sorting algorithm, which requires O(N log2 N) basic sorters to sort N inputs. While the asymptotic complexity (in terms of the required number of sorters) of our sorting algorithm is the same as the SS-Mk, for wide ranges of N, our algorithm requires fewer sorters than the SS-Mk. Finally, we consider a binary sorting network, where the basic sorter is implemented in threshold logic and scales linearly with the number of inputs, and compare the complexity in terms of the required number of gates. For wide ranges of N, our algorithm requires fewer gates than the SS-Mk.
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