New Bounds on Optimal Sorting Networks

TL;DR

This paper introduces new parallel sorting networks for 17 to 20 inputs, achieving faster and optimal solutions for certain input sizes, thus advancing the understanding of minimal depth sorting networks.

Contribution

It provides the first known optimal sorting network for 17 inputs and improved networks for 19 and 20 inputs, reducing the upper bounds on their minimal depth.

Findings

New sorting networks for 17-20 inputs with fewer steps

Optimal network established for 17 inputs

Improved upper bounds for 19 and 20 inputs

Abstract

We present new parallel sorting networks for $17$ to $20$ inputs. For $17, 19,$ and $20$ inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on $17, 19,$ and $20$ channels. Furthermore, we show that our sorting network for $17$ inputs is optimal in the sense that no sorting network using less layers exists. This solves the main open problem of [D. Bundala & J. Za\'vodn\'y. Optimal sorting networks, Proc. LATA 2014].