Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy

TL;DR

This paper introduces a novel balanced coarsening scheme for multilevel hypergraph partitioning that leverages Wasserstein discrepancy and optimal transport to improve partition quality and balance.

Contribution

It presents a new coarsening method using Wasserstein discrepancy and an initial partitioning algorithm based on a concave normalized cut function.

Findings

The coarsening scheme effectively minimizes connectivity metrics.

The initial partitioning algorithm improves partition quality under balance constraints.

The approach outperforms existing methods in hypergraph partitioning quality.

Abstract

We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT algorithm, we generate a prior hypergraph under a relaxed balance constraint. With the prior hypergraph, we have defined the Wasserstein discrepancy to coordinate the optimal transport of coarsening process. And the optimal transport matrix is solved by Sinkhorn algorithm. Our coarsening scheme fully takes into account the minimization of connectivity metric (objective function). For the initial partitioning stage, we define a normalized cut function induced by Fiedler vector, which is theoretically proved to be a concave function. Thereby, a three-point algorithm is designed to find the best cut under the balance constraint.