Sorting Networks: The Final Countdown

TL;DR

This paper introduces new pruning techniques and an algorithm to efficiently search for minimal depth sorting networks, successfully finding optimal solutions for up to 12 inputs.

Contribution

It presents novel pruning methods for the last four levels of sorting networks and an algorithm to determine their existence, improving search efficiency.

Findings

Successfully found optimal depth sorting networks for all n ≤ 12

Developed new pruning techniques based on output set representations

Validated the algorithm through extensive experiments

Abstract

In this paper we extend the knowledge on the problem of empirically searching for sorting networks of minimal depth. We present new search space pruning techniques for the last four levels of a candidate sorting network by considering only the output set representation of a network. We present an algorithm for checking whether an $n$-input sorting network of depth $d$ exists by considering the minimal up to permutation and reflection itemsets at each level and using the pruning at the last four levels. We experimentally evaluated this algorithm to find the optimal depth sorting networks for all $n \leq 12$.