# Evaluation of a Flow-Based Hypergraph Bipartitioning Algorithm

## TL;DR

This paper introduces HyperFlowCutter, a flow-based hypergraph bipartitioning algorithm, and demonstrates its effectiveness as a fast refinement method that improves partition quality with competitive speed.

## Contribution

The paper presents ReBaHFC, a novel hypergraph partitioning approach combining multilevel partitioning with HyperFlowCutter refinement, offering a new speed-quality trade-off.

## Key findings

- ReBaHFC significantly improves solution quality over initial partitions.
- ReBaHFC is one order of magnitude faster than top hypergraph partitioners.
- For perfectly balanced bipartitions, HyperFlowCutter slightly outperforms ReBaHFC.

## Abstract

In this paper, we propose HyperFlowCutter, an algorithm for balanced hypergraph bipartitioning. It is based on minimum S-T hyperedge cuts and maximum flows. It computes a sequence of bipartitions that optimize cut size and balance in the Pareto sense, being able to trade one for the other. HyperFlowCutter builds on the FlowCutter algorithm for partitioning graphs. We propose additional features, such as handling disconnected hypergraphs, novel methods for obtaining starting S,T pairs as well as an approach to refine a given partition with HyperFlowCutter. Our main contribution is ReBaHFC, a new algorithm which obtains an initial partition with the fast multilevel hypergraph partitioner PaToH and then improves it using HyperFlowCutter as a refinement algorithm. ReBaHFC is able to significantly improve the solution quality of PaToH at little additional running time. The solution quality is only marginally worse than that of the best-performing hypergraph partitioners KaHyPar and hMETIS, while being one order of magnitude faster. Thus ReBaHFC offers a new time-quality trade-off in the current spectrum of hypergraph partitioners. For the special case of perfectly balanced bipartitioning, only the much slower plain HyperFlowCutter yields slightly better solutions than ReBaHFC, while only PaToH is faster than ReBaHFC.