Depth-13 Sorting Networks for 28 Channels

TL;DR

This paper presents a new depth-13 sorting network for 28 channels, improving the previous best and using a combination of symmetry, greedy extension, and SAT solving techniques.

Contribution

It introduces the first depth-13 sorting network for 28 channels, utilizing symmetry, greedy extension, and SAT solving to optimize network depth.

Findings

Achieved a new depth upper bound of 13 for 28-channel sorting networks.

Constructed the network by combining high-quality prefixes and extending them greedily.

Used SAT solvers to complete the network layers efficiently.

Abstract

We establish new depth upper bounds for sorting networks on 27 and 28 channels, improving the previous best bound of 14 to 13. Our 28-channel network is constructed with reflectional symmetry by combining high-quality prefixes of 16- and 12-channel networks, extending them greedily one comparator at a time, and using a SAT solver to complete the remaining layers.