Sorting Networks: the End Game

TL;DR

This paper explores the properties of the back end of sorting networks to improve the search for optimal size and depth, significantly enhancing solver efficiency compared to previous front-end focused methods.

Contribution

It introduces new properties of the back end of sorting networks, aiding in understanding and optimizing their design, which was previously overlooked.

Findings

Back-end properties improve understanding of sorting networks

New properties speed up optimal network search by an order of magnitude

Enhanced solvers for size and depth optimization

Abstract

This paper studies properties of the back end of a sorting network and illustrates the utility of these in the search for networks of optimal size or depth. All previous works focus on properties of the front end of networks and on how to apply these to break symmetries in the search. The new properties help shed understanding on how sorting networks sort and speed-up solvers for both optimal size and depth by an order of magnitude.