An Improved Subsumption Testing Algorithm for the Optimal-Size Sorting Network Problem

TL;DR

This paper introduces a novel bipartite graph-based method for subsumption testing in optimal-size sorting network problems, significantly improving efficiency and enabling verification of optimal networks with 9 channels.

Contribution

The paper presents a new bipartite graph model for subsumption testing, reducing computation time by over tenfold and confirming optimality of a 25-comparator network for 9 channels.

Findings

Reduced subsumption check time by more than 10 times

Successfully generated all filters for 9-channel networks

Confirmed the optimality of the 25-comparator network

Abstract

In this paper a new method for checking the subsumption relation for the optimal-size sorting network problem is described. The new approach is based on creating a bipartite graph and modelling the subsumption test as the problem of enumerating all perfect matchings in this graph. Experiments showed significant improvements over the previous approaches when considering the number of subsumption checks and the time needed to find optimal-size sorting networks. We were able to generate all the complete sets of filters for comparator networks with 9 channels, confirming that the 25-comparators sorting network is optimal. The running time was reduced more than 10 times, compared to the state-of-the-art results.