Symmetry-breaking symmetry in directed spectral partitioning

TL;DR

This paper introduces a novel symmetry-breaking technique in directed spectral partitioning that enhances the creation of acyclic partitions and topological orders, significantly outperforming existing algorithms in reuse distance and linear arrangement.

Contribution

It presents a new symmetry-breaking method for directed spectral partitioning that improves acyclic partitioning and topological ordering, surpassing state-of-the-art algorithms.

Findings

Outperforms Gorder algorithm by up to 17x in reuse distance

Generates acyclic bi-partitions and topological orders with high locality

Achieves superior results in linear arrangement tasks

Abstract

We break the symmetry in classical spectral bi-partitioning in order to incentivise the alignment of directed cut edges. We use this to generate acyclic bi-partitions and furthermore topological orders of directed acyclic graphs with superb locality. The new approach outperforms the state-of-the-art Gorder algorithm by up to $17\times$ on total reuse distance and minimum linear arrangement.