Network Flow-Based Refinement for Multilevel Hypergraph Partitioning

TL;DR

This paper introduces a flow-based refinement framework for multilevel hypergraph partitioning that enhances solution quality while maintaining efficient runtime, applicable across diverse benchmark hypergraphs.

Contribution

It generalizes a graph flow-based improvement algorithm to hypergraphs and integrates it into KaHyPar, improving partition quality and efficiency.

Findings

Achieves better partition quality on benchmark hypergraphs.

Maintains runtime comparable to existing tools like hMetis.

Effectively reduces hypergraph flow network sizes.

Abstract

We present a refinement framework for multilevel hypergraph partitioning that uses max-flow computations on pairs of blocks to improve the solution quality of a $k$-way partition. The framework generalizes the flow-based improvement algorithm of KaFFPa from graphs to hypergraphs and is integrated into the hypergraph partitioner KaHyPar. By reducing the size of hypergraph flow networks, improving the flow model used in KaFFPa, and developing techniques to improve the running time of our algorithm, we obtain a partitioner that computes the best solutions for a wide range of benchmark hypergraphs from different application areas while still having a running time comparable to that of hMetis.