# Advanced Flow-Based Multilevel Hypergraph Partitioning

arXiv: https://arxiv.org/abs/2003.12110 · HTML: https://mlsanity.com/paper/2003.12110/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [More Recent Advances in (Hyper)Graph Partitioning](https://mlsanity.com/paper/2205.13202/) (2022)
- [Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy](https://mlsanity.com/paper/2106.07501/) (2021)
- [A Multi-Level Framework for Multi-Objective Hypergraph Partitioning: Combining Minimum Spanning Tree and Proximal Gradient](https://mlsanity.com/paper/2509.22294/) (2025)

## Abstract (arXiv)

The balanced hypergraph partitioning problem is to partition a hypergraph into k disjoint blocks of bounded size such that the sum of the number of blocks connected by each hyperedge is minimized. We present an improvement to the flow-based refinement framework of KaHyPar-MF, the current state-of-the-art multilevel k-way hypergraph partitioning algorithm for high-quality solutions. Our improvement is based on the recently proposed HyperFlowCutter algorithm for computing bipartitions of unweighted hypergraphs by solving a sequence of incremental maximum flow problems. Since vertices and hyperedges are aggregated during the coarsening phase, refinement algorithms employed in the multilevel setting must be able to handle both weighted hyperedges and weighted vertices -- even if the initial input hypergraph is unweighted. We therefore enhance HyperFlowCutter to handle weighted instances and propose a technique for computing maximum flows directly on weighted hypergraphs. We compare the performance of two configurations of our new algorithm with KaHyPar-MF and seven other partitioning algorithms on a comprehensive benchmark set with instances from application areas such as VLSI design, scientific computing, and SAT solving. Our first configuration, KaHyPar-HFC, computes slightly better solutions than KaHyPar-MF using significantly less running time. The second configuration, KaHyPar-HFC*, computes solutions of significantly better quality and is still slightly faster than KaHyPar-MF. Furthermore, in terms of solution quality, both configurations also outperform all other competing partitioners.