Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

TL;DR

This paper introduces algebraic distance as a new measure for hypergraph coarsening, improving multilevel partitioning methods with extensive experiments and a new benchmark for solver comparison.

Contribution

It presents a novel algebraic distance measure for hypergraph coarsening and demonstrates its effectiveness in multilevel partitioning algorithms.

Findings

Algebraic distance improves hypergraph coarsening quality

The proposed method outperforms existing solvers in experiments

A new benchmark for hypergraph partitioning is introduced

Abstract

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coarsening stage of multilevel hypergraph partitioning solvers. The algebraic distance is a vertex distance measure that extends hyperedge weights for capturing the local connectivity of vertices which is critical for hypergraph coarsening schemes. The practical effectiveness of the proposed measure and corresponding coarsening scheme is demonstrated through extensive computational experiments on a diverse set of problems. Finally, we propose a benchmark of hypergraph partitioning problems to compare the quality of other solvers.