Document Open Access Logo

Engineering Learned Heuristics to Improve Clustering for Multilevel Graph Partitioning

Authors Simeon Schrape , Nikolai Maas , Kenneth Langedal , Daniel Seemaier

PDF

File

Thumbnail PDF
PDF
LIPIcs.SEA.2026.25.pdf
  • Filesize: 1.47 MB
  • 21 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Graph Partitioning
  • Graph Algorithms
  • Machine Learning
  • Neural Networks

Metrics

Abstract

Balanced Graph Partitioning is a classical optimization problem where quality guarantees are computationally infeasible, and practical solvers therefore rely on manually engineered heuristics. Yet, the problem has also proven difficult for approaches that rely heavily on machine learning - especially since applications often need to partition graphs of huge scale in a short amount of time. Instead, we demonstrate how to achieve practical improvements with a more careful approach that uses machine learning to improve heuristic decisions within the state-of-the-art solver Mt-KaHyPar.
We use a pre-trained neural network to predict a score for each edge, which then guides clustering decisions in the first phase of the partitioning (the coarsening). Combined with corresponding adjustments to the clustering algorithm and an efficient implementation of the neural network logic, we improve the overall solution quality while preserving the efficiency and scalability of the original algorithm. Our detailed evaluation on more than 180 graphs shows an average quality improvement of 2% on a class of graphs with beneficial properties, and unchanged quality on all remaining graphs. Moreover, our improvements generalize to a set of instances from the literature that are much larger than the graphs used during training.

Cite As Get BibTex

Simeon Schrape, Nikolai Maas, Kenneth Langedal, and Daniel Seemaier. Engineering Learned Heuristics to Improve Clustering for Multilevel Graph Partitioning. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 25:1-25:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SEA.2026.25

Author Details

Simeon Schrape
  • Karlsruhe Institute of Technology, Germany
Nikolai Maas
  • Karlsruhe Institute of Technology, Germany
Kenneth Langedal
  • Faculty of Mathematics and Computer Science, Heidelberg University, Germany
Daniel Seemaier
  • Karlsruhe Institute of Technology, Germany

Funding

  • Langedal, Kenneth: Supported by DFG grant SCHU 2567/5-1.

Supplementary Materials

References

  1. Yaroslav Akhremtsev, Tobias Heuer, Peter Sanders, and Sebastian Schlag. Engineering a Direct k-way Hypergraph Partitioning Algorithm. In 19th Workshop on Algorithm Engineering & Experiments (ALENEX), pages 28-42, 2017. URL: https://doi.org/10.1137/1.9781611974768.3.
  2. Yaroslav Akhremtsev, Peter Sanders, and Christian Schulz. High-Quality Shared-Memory Graph Partitioning. IEEE Transactions on Parallel Distributed Systems, 31(11):2710-2722, 2020. URL: https://doi.org/10.1109/TPDS.2020.3001645.
  3. Robin Andre, Sebastian Schlag, and Christian Schulz. Memetic Multilevel Hypergraph Partitioning. In Genetic and Evolutionary Computation Conference, (GECCO), pages 347-354, 2018. URL: https://doi.org/10.1145/3205455.3205475.
  4. David A. Bader, Henning Meyerhenke, Peter Sanders, and Dorothea Wagner. Graph Partitioning and Graph Clustering, volume 588. American Mathematical Society, 2013. URL: https://doi.org/10.1090/conm/588.
  5. Thomas D. Barrett, Christopher W.F. Parsonson, and Alexandre Laterre. Learning to Solve Combinatorial Graph Partitioning Problems via Efficient Exploration. arXiv preprint, 2022. URL: https://doi.org/10.48550/arXiv.2205.14105.
  6. Vincent D. Blondel, Jean Guillaume, Renaud Lambiotte, and Etienne Lefebvre. Fast Unfolding of Communities in Large Networks. Journal of Statistical Mechanics: Theory and Experiment, 2008. URL: https://doi.org/10.1088/1742-5468/2008/10/P10008.
  7. Aydin Buluç, Henning Meyerhenke, Ilya Safro, Peter Sanders, and Christian Schulz. Recent Advances in Graph Partitioning. In Algorithm Engineering, volume 9220, pages 117-158. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-49487-6_4.
  8. Chen Cai, Dingkang Wang, and Yusu Wang. Graph Coarsening with Neural Networks. In 9th International Conference on Learning Representations (ICLR), 2021. Google Scholar
  9. Ümit Çatalyürek, Karen Devine, Marcelo Faraj, Lars Gottesbüren, Tobias Heuer, Henning Meyerhenke, Peter Sanders, Sebastian Schlag, Christian Schulz, Daniel Seemaier, et al. More Recent Advances in (Hyper)Graph Partitioning. ACM Computing Surveys, 55(12):253-253, 2023. URL: https://doi.org/10.1145/3571808.
  10. Umit V. Catalyürek, Mehmet Deveci, Kamer Kaya, and Bora Uçar. Multithreaded Clustering for Multi-level Hypergraph Partitioning. In 26th International Parallel and Distributed Processing Symposium (IPDPS), pages 848-859. IEEE Computer Society, 2012. URL: https://doi.org/10.1109/IPDPS.2012.81.
  11. Cédric Chevalier and François Pellegrini. PT-Scotch: A Tool for Efficient Parallel Graph Ordering. Parallel Computing, 34(6-8):318-331, 2008. URL: https://doi.org/10.1016/j.parco.2007.12.001.
  12. Cédric Chevalier and Ilya Safro. Comparison of Coarsening Schemes for Multilevel Graph Partitioning. In 3rd Conference on Learning and Intelligent Optimization (LION), volume 5851, pages 191-205. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-11169-3_14.
  13. Timothy A. Davis and Yifan Hu. The University of Florida Sparse Matrix Collection. ACM Transactions on Mathematical Software, 38(1):1:1-1:25, 2011. URL: https://doi.org/10.1145/2049662.2049663.
  14. Elizabeth D. Dolan and Jorge J. Moré. Benchmarking Optimization Software with Performance Profiles. Mathematical Programming, 91(2):201-213, 2002. URL: https://doi.org/10.1007/s101070100263.
  15. Charles M. Fiduccia and Robert M. Mattheyses. A Linear-Time Heuristic for Improving Network Partitions. In 19th Design Automation Conference (DAC), pages 175-181, 1982. URL: https://doi.org/10.1145/800263.809204.
  16. Alice Gatti, Zhixiong Hu, Tess Smidt, Esmond G. Ng, and Pieter Ghysels. Graph Partitioning and Sparse Matrix Ordering using Reinforcement Learning and Graph Neural Networks. Journal of Machine Learning Research, 23(303):1-28, 2022. URL: https://jmlr.org/papers/v23/21-0644.html.
  17. Michael S. Gilbert, Kamesh Madduri, Erik G. Boman, and Siva Rajamanickam. Jet: Multilevel Graph Partitioning on Graphics Processing Units. SIAM Journal of Scientific Computing., 46(5):700, 2024. URL: https://doi.org/10.1137/23M1559129.
  18. Michael S. Gilbert, Kamesh Madduri, Erik G. Boman, and Sivasankaran Rajamanickam. Jet: Multilevel Graph Partitioning on GPUs, 2023. URL: https://doi.org/10.48550/arXiv.2304.13194.
  19. Kazushige Goto and Robert A. van de Geijn. Anatomy of High-Performance Matrix Multiplication. ACM Transactions on Mathematical Software (TOMS), 34(3):1-25, 2008. URL: https://doi.org/10.1145/1356052.1356053.
  20. Lars Gottesbüren, Tobias Heuer, Nikolai Maas, Peter Sanders, and Sebastian Schlag. Scalable High-Quality Hypergraph Partitioning. ACM Transactions on Algorithms, 20(1):9:1-9:54, 2024. URL: https://doi.org/10.1145/3626527.
  21. Lars Gottesbüren, Nikolai Maas, Dominik Rosch, Peter Sanders, and Daniel Seemaier. Linear-Time Multilevel Graph Partitioning via Edge Sparsification. In 33th European Symposium on Algorithms (ESA), volume 351, pages 32:1-32:20, 2025. URL: https://doi.org/10.4230/LIPIcs.ESA.2025.32.
  22. Lars Gottesbüren, Tobias Heuer, Peter Sanders, and Sebastian Schlag. Scalable Shared-Memory Hypergraph Partitioning. In 23st Workshop on Algorithm Engineering & Experiments (ALENEX), 2021. URL: https://doi.org/10.1137/1.9781611976472.2.
  23. Lars Gottesbüren, Tobias Heuer, Peter Sanders, Christian Schulz, and Daniel Seemaier. Deep Multilevel Graph Partitioning. In 29th European Symposium on Algorithms (ESA), pages 48:1-48:17, 2021. URL: https://doi.org/10.4230/LIPIcs.ESA.2021.48.
  24. Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive Representation Learning on Large Graphs. In 31th Conference on Neural Information Processing Systems (NIPS 2017), pages 1-11. Curran Associates, 2017. Google Scholar
  25. Tobias Heuer, Lars Gottesbüren, Nikolai Maas, and Simeon Schrape. Mt-KaHyPar. Software, version 1.5.3., (visited on 2026-05-29). URL: https://github.com/kahypar/mt-kahypar/tree/sea2026
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.26212
  26. Tobias Heuer and Sebastian Schlag. Improving Coarsening Schemes for Hypergraph Partitioning by Exploiting Community Structure. In 16th International Symposium on Experimental Algorithms (SEA), pages 21:1-21:19, June 2017. URL: https://doi.org/10.4230/LIPIcs.SEA.2017.21.
  27. George Karypis and Vipin Kumar. A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. SIAM Journal on Scientific Computing, 20(1):359-392, 1998. URL: https://doi.org/10.1137/S1064827595287997.
  28. George Karypis and Vipin Kumar. Parallel Multilevel k-Way Partitioning Scheme for Irregular Graphs. Siam Review, 41(2):278-300, 1999. URL: https://doi.org/10.1137/S0036144598334138.
  29. Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization, 2017. URL: https://doi.org/10.48550/arXiv.1412.6980.
  30. Thomas N. Kipf and Max Welling. Semi-Supervised Classification with Graph Convolutional Networks. In 5th International Conference on Learning Representations (ICLR), 2017. Google Scholar
  31. Kenneth Langedal and Fredrik Manne. Graph Neural Networks as Ordering Heuristics for Parallel Graph Coloring. In 27st Workshop on Algorithm Engineering & Experiments (ALENEX), pages 56-67. Society for Industrial and Applied Mathematics, 2025. URL: https://doi.org/10.1137/1.9781611978339.5.
  32. Dominique Lasalle and George Karypis. Multi-threaded Graph Partitioning. In 27th IEEE International Symposium on Parallel and Distributed Processing (IPDPS), pages 225-236, 2013. URL: https://doi.org/10.1109/IPDPS.2013.50.
  33. Dominique LaSalle, Md. Mostofa Ali Patwary, Nadathur Satish, Narayanan Sundaram, Pradeep Dubey, and George Karypis. Improving Graph Partitioning for Modern Graphs and Architectures. In 5th Workshop on Irregular Applications - Architectures and Algorithms (IA3), pages 14:1-14:4. ACM, 2015. URL: https://doi.org/10.1145/2833179.2833188.
  34. Andreas Loukas. What Graph Neural Networks Cannot Learn: Depth vs Width. In 8th International Conference on Learning Representations (ICLR), 2020. Google Scholar
  35. Nikolai Maas, Lars Gottesbüren, and Daniel Seemaier. Parallel Unconstrained Local Search for Partitioning Irregular Graphs. In 26st Workshop on Algorithm Engineering & Experiments (ALENEX), pages 32-45. SIAM, 2024. URL: https://doi.org/10.1137/1.9781611977929.3.
  36. Nikolai Maas, Lars Gottesbüren, and Daniel Seemaier. Benchmark Sets and Experimental Results for "Parallel Unconstrained Local Search for Partitioning Irregular Graphs" , May 2025. URL: https://doi.org/10.5281/zenodo.15386627.
  37. Henning Meyerhenke, Peter Sanders, and Christian Schulz. Partitioning Complex Networks via Size-Constrained Clustering. In 13th International Symposium on Experimental Algorithms (SEA), pages 351-363. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-07959-2_30.
  38. Henning Meyerhenke, Peter Sanders, and Christian Schulz. Parallel Graph Partitioning for Complex Networks. IEEE Transactions on Parallel and Distributed Systems, 28(9):2625-2638, 2017. URL: https://doi.org/10.1109/TPDS.2017.2671868.
  39. Azade Nazi, Will Hang, Anna Goldie, Sujith Ravi, and Azalia Mirhoseini. GAP: Generalizable Approximate Graph Partitioning Framework. arXiv preprint, 2019. URL: https://doi.org/10.48550/arXiv.1903.00614.
  40. Chuck Pheatt. Intel Threading Building Blocks. Journal of Computing Sciences in Colleges, 23(4):298-298, 2008. Google Scholar
  41. Ryan A. Rossi and Nesreen K. Ahmed. The Network Data Repository with Interactive Graph Analytics and Visualization. In 29th Conference on Artificial Intelligence (AAAI), 2015. URL: https://doi.org/10.1609/AAAI.V29I1.9277.
  42. Ilya Safro, Dorit Ron, and Achi Brandt. Multilevel algorithms for linear ordering problems. ACM J. Exp. Algorithmics, 13, 2008. URL: https://doi.org/10.1145/1412228.1412232.
  43. Ilya Safro, Peter Sanders, and Christian Schulz. Advanced coarsening schemes for graph partitioning. ACM J. Exp. Algorithmics, 19(1), 2014. URL: https://doi.org/10.1145/2670338.
  44. Peter Sanders and Daniel Seemaier. Brief Announcement: Distributed Unconstrained Local Search for Multilevel Graph Partitioning. In 36th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 443-445. ACM, 2024. URL: https://doi.org/10.1145/3626183.3660257.
  45. Sebastian Schlag, Vitali Henne, Tobias Heuer, Henning Meyerhenke, Peter Sanders, and Christian Schulz. k-way Hypergraph Partitioning via n-Level Recursive Bisection. In 18th Workshop on Algorithm Engineering & Experiments (ALENEX), pages 53-67. SIAM, 2016. URL: https://doi.org/10.1137/1.9781611974317.5.
  46. Sebastian Schlag, Tobias Heuer, Lars Gottesbüren, Yaroslav Akhremtsev, Christian Schulz, and Peter Sanders. High-Quality Hypergraph Partitioning. ACM Journal of Experimental Algorithmics, 27:1.9:1-1.9:39, 2022. URL: https://doi.org/10.1145/3529090.
  47. Alan J. Soper, Chris Walshaw, and Mark Cross. A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-Partitioning. Journal of Global Optimization, 29(2):225-241, 2004. URL: https://doi.org/10.1023/B:JOGO.0000042115.44455.F3.
  48. Natarajan Viswanathan, Charles J. Alpert, Cliff C. N. Sze, Zhuo Li, and Yaoguang Wei. The DAC 2012 Routability-Driven Placement Contest and Benchmark Suite. In 49th Conference on Design Automation (DAC), pages 774-782. ACM, 2012. URL: https://doi.org/10.1145/2228360.2228500.
  49. Chris Walshaw, Mark Cross, and Martin G. Everett. Parallel Dynamic Graph Partitioning for Adaptive Unstructured Meshes. Journal of Parallel and Distributed Computing, 47(2):102-108, 1997. URL: https://doi.org/10.1006/jpdc.1997.1407.
  50. Pengcheng Wei, Yuan Fang, Zhihao Wen, Zheng Xiao, and Binbin Chen. An end-to-end bi-objective approach to deep graph partitioning. Neural Networks, 181:106823, 2025. URL: https://doi.org/10.1016/j.neunet.2024.106823.
  51. Ümit V. Catalyürek and Cevdet Aykanat. Hypergraph-Partitioning-based Decomposition for Parallel Sparse-Matrix Vector Multiplication. IEEE Transactions on Parallel and Distributed Systems, 10(7):673-693, 1999. URL: https://doi.org/10.1109/71.780863.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact