An Enhanced Multiway Sorting Network Based on n-Sorters

TL;DR

This paper introduces an improved multiway sorting network using n-sorters, reducing the number of sorters and latency compared to existing methods, and demonstrates efficiency in both sorting and gate complexity.

Contribution

It proposes a new n-sorter based multiway merging algorithm and a sorting algorithm with fewer sorters and gates than prior approaches like SS-Mk.

Findings

Requires fewer sorters than SS-Mk for many N.

Achieves O(N log2 N) complexity in sorters.

Reduces gate complexity in threshold logic implementation.

Abstract

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.