Symmetry-breaking symmetry in directed spectral partitioning

2025-08-22

AI Summary

Classical spectral bisection suffers from symmetry-induced ambiguities in directed graph partitioning, leading to disordered cut-edge orientations and poor-quality topological orderings. Method: This paper introduces, for the first time, a symmetry-breaking mechanism into spectral partitioning of directed graphs. It enforces directional constraints to align cut edges consistently, enabling acyclic bisection and high-locality topological sorting. The approach integrates a direction-aware Laplacian operator with the Minimum Linear Arrangement (MLA) objective, grounded in directed spectral graph theory. Results: Experiments demonstrate that our method improves total reuse distance and MLA score by up to 17× over the state-of-the-art Gorder algorithm. It significantly enhances structural locality and ordering quality, establishing a novel paradigm for efficient compilation scheduling and memory locality optimization on directed acyclic graphs.

Technology Category

Machine Learning: Graph-based Machine LearningConstraint Satisfaction and Optimization: Distributed CSP/OptimizationPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Bridging structured and unstructured dataSemantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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 $17 imes$ on total reuse distance and minimum linear arrangement.

Problem

• Breaking symmetry in spectral bi-partitioning for directed edges
• Generating acyclic bi-partitions with superb locality
• Outperforming Gorder algorithm on reuse distance metrics

Innovation

• Directed spectral partitioning breaks symmetry
• Generates acyclic bipartitions with superb locality
• Outperforms Gorder algorithm by 17x