Parallel Flow-Based Hypergraph Partitioning

Authors Lars Gottesbüren, Tobias Heuer, Peter Sanders

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Author Details

Lars Gottesbüren
  • Karlsruhe Institute of Technology, Karlsruhe, Germany
Tobias Heuer
  • Karlsruhe Institute of Technology, Karlsruhe, Germany
Peter Sanders
  • Karlsruhe Institute of Technology, Karlsruhe, Germany

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Lars Gottesbüren, Tobias Heuer, and Peter Sanders. Parallel Flow-Based Hypergraph Partitioning. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We present a shared-memory parallelization of flow-based refinement, which is considered the most powerful iterative improvement technique for hypergraph partitioning at the moment. Flow-based refinement works on bipartitions, so current sequential partitioners schedule it on different block pairs to improve k-way partitions. We investigate two different sources of parallelism: a parallel scheduling scheme and a parallel maximum flow algorithm based on the well-known push-relabel algorithm. In addition to thoroughly engineered implementations, we propose several optimizations that substantially accelerate the algorithm in practice, enabling the use on extremely large hypergraphs (up to 1 billion pins). We integrate our approach in the state-of-the-art parallel multilevel framework Mt-KaHyPar and conduct extensive experiments on a benchmark set of more than 500 real-world hypergraphs, to show that the partition quality of our code is on par with the highest quality sequential code (KaHyPar), while being an order of magnitude faster with 10 threads.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Hypergraphs
  • Mathematics of computing → Graph algorithms
  • multilevel hypergraph partitioning
  • shared-memory algorithms
  • maximum flow


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