Document Open Access Logo

High-Quality Multi-Constraint Hypergraph Partitioning via Greedy Rebalancing

Author Nikolai Maas

PDF

File

Thumbnail PDF
PDF
LIPIcs.ESA.2026.12.pdf
  • Filesize: 1.18 MB
  • 17 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Hypergraph Partitioning
  • Multi-Constraint Partitioning
  • Graph Algorithms
  • Multilevel Algorithms
  • Local Search
  • Vector Scheduling
  • Multidimensional Load Balancing

Metrics

Abstract

Multi-constraint hypergraph partitioning is a generalization of balanced partitioning, where the vertex set of a hypergraph is partitioned such that the inter-block connectivity of hyperedges is minimized while balancing the vertices with regard to d distinct constraints. A prominent class of applications is data distribution tasks, where this allows to achieve good load balance for d different kinds of resources and simultaneously minimize the communication volume.
Although the best approaches for single-constraint partitioning are usually complex (multilevel) algorithms with many components, we show that replacing only one component already leads to high-quality multi-constraint partitions: the rebalancing step, which restores balance for a partition that has (hopefully) small connectivity but violates the constraints. We design a multi-constraint rebalancing algorithm based on greedy local search, proving that balance is always restored for d = 2 and bounded maximum weight. The key is to ensure monotonically decreasing global imbalance by choosing an imbalance metric where there is always a balance-improving move available. Integrating our algorithm into the state-of-the-art partitioner Mt-KaHyPar, we demonstrate an 11.5 % geometric mean connectivity reduction compared to the next best competitor (Metis) and better reliability regarding partition balance, even though the majority of inputs is outside of the theoretical guarantee.

Cite As Get BibTex

Nikolai Maas. High-Quality Multi-Constraint Hypergraph Partitioning via Greedy Rebalancing. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.12

Author Details

Nikolai Maas
  • Karlsruhe Institute of Technology, Germany

Supplementary Materials

References

  1. Charles J. Alpert. The ISPD98 Circuit Benchmark Suite. In International Symposium on Physical Design (ISPD), pages 80-85, April 1998. URL: https://doi.org/10.1145/274535.274546.
  2. Konstantin Andreev and Harald Räcke. Balanced Graph Partitioning. In 16th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 120-124, 2004. URL: https://doi.org/10.1145/1007912.1007931.
  3. Ankita Atrey, Gregory van Seghbroeck, Higinio Mora, Bruno Volckaert, and Filip De Turck. UnifyDR: A Generic Framework for Unifying Data and Replica Placement. IEEE Access, 8:216894-216910, 2020. URL: https://doi.org/10.1109/ACCESS.2020.3041670.
  4. Dmitrii Avdiukhin, Sergey Pupyrev, and Grigory Yaroslavtsev. Multi-Dimensional Balanced Graph Partitioning via Projected Gradient Descent. Proceedings of the VLDB Endowment, 12(8):906-919, 2019. URL: https://doi.org/10.14778/3324301.3324307.
  5. Cevdet Aykanat, Berkant Barla Cambazoglu, and Bora Uçar. Multi-level Direct k-way Hypergraph Partitioning With Multiple Constraints and Fixed Vertices. Journal of Parallel and Distributed Computing, 68(5):609-625, 2008. URL: https://doi.org/10.1016/j.jpdc.2007.09.006.
  6. Nikhil Bansal, Tim Oosterwijk, Tjark Vredeveld, and Ruben van der Zwaan. Approximating Vector Scheduling: Almost Matching Upper and Lower Bounds. Algorithmica, 76(4):1077-1096, 2016. URL: https://doi.org/10.1007/S00453-016-0116-0.
  7. Rémi Barat, Cédric Chevalier, and François Pellegrini. Multi-criteria Graph Partitioning with Scotch. In 8th Workshop on Combinatorial Scientific Computing (CSC), pages 66-75, 2018. URL: https://doi.org/10.1137/1.9781611975215.7.
  8. 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.
  9. Ismail Bustany, Grigor Gasparyan, Andrew B. Kahng, Ioannis Koutis, Bodhisatta Pramanik, and Zhiang Wang. An Open-Source Constraints-Driven General Partitioning Multi-Tool for VLSI Physical Design. In International Conference on Computer Aided Design (ICCAD), pages 1-9, 2023. URL: https://doi.org/10.1109/ICCAD57390.2023.10323975.
  10. 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.
  11. Chandra Chekuri and Sanjeev Khanna. On Multidimensional Packing Problems. SIAM Journal on Computing, 33(4):837-851, 2004. URL: https://doi.org/10.1137/S0097539799356265.
  12. Carlo Curino, Yang Zhang, Evan P. C. Jones, and Samuel Madden. Schism: a Workload-Driven Approach to Database Replication and Partitioning. Proceedings of the VLDB Endowment, 3(1):48-57, 2010. URL: https://doi.org/10.14778/1920841.1920853.
  13. Karen D. Devine, Erik G. Boman, Robert T. Heaphy, Rob H. Bisseling, and Ümit V. Catalyürek. Parallel Hypergraph Partitioning for Scientific Computing. In 20th International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2006. URL: https://doi.org/10.1109/IPDPS.2006.1639359.
  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. Shantanu Dutt and Wenyong Deng. Cluster-Aware Iterative Improvement Techniques for Partitioning Large VLSI Circuits. ACM Transactions on Design Automation of Electronic Systems, 7(1):91-121, 2002. URL: https://doi.org/10.1145/504914.504918.
  16. 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.
  17. Jonas Fietz, Mathias J. Krause, Christian Schulz, Peter Sanders, and Vincent Heuveline. Optimized Hybrid Parallel Lattice Boltzmann Fluid Flow Simulations on Complex Geometries. In 18th European Conference on Parallel Processing (Euro-Par), volume 7484 of Lecture Notes in Computer Science, pages 818-829, 2012. URL: https://doi.org/10.1007/978-3-642-32820-6_81.
  18. 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.
  19. 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.
  20. Lars Gottesbüren, Tobias Heuer, and Peter Sanders. Parallel Flow-Based Hypergraph Partitioning. In 20th International Symposium on Experimental Algorithms (SEA), volume 233, pages 5:1-5:21, 2022. URL: https://doi.org/10.4230/LIPIcs.SEA.2022.5.
  21. Lars Gottesbüren, Tobias Heuer, Peter Sanders, and Sebastian Schlag. Shared-Memory n-level Hypergraph Partitioning. In 24st Workshop on Algorithm Engineering & Experiments (ALENEX), 2022. URL: https://doi.org/10.1137/1.9781611977042.11.
  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. Wenzhong Guo, Genggeng Liu, Guolong Chen, and Shaojun Peng. A Hybrid Multi-Objective PSO Algorithm with Local Search Strategy for VLSI Partitioning. Frontiers of Computer Science, 8(2):203-216, 2014. URL: https://doi.org/10.1007/S11704-014-3008-Y.
  25. Tobias Heuer, Nikolai Maas, and Sebastian Schlag. Multilevel Hypergraph Partitioning with Vertex Weights Revisited. In 19th International Symposium on Experimental Algorithms (SEA), pages 8:1-8:20, 2021. URL: https://doi.org/10.4230/LIPIcs.SEA.2021.8.
  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. Multilevel Algorithms for Multi-Constraint Hypergraph Partitioning. Technical report, University of Minnesota, 1999. Google Scholar
  28. George Karypis and Vipin Kumar. Multilevel Algorithms for Multi-Constraint Graph Partitioning. In ACM/IEEE Conference on Supercomputing (SC), page 28, 1998. URL: https://doi.org/10.1109/SC.1998.10018.
  29. Robert Krause, Lars Gottesbüren, and Nikolai Maas. Deterministic Parallel High-Quality Hypergraph Partitioning. In 3rd Conference on Applied and Computational Discrete Algorithms (ACDA), pages 222-236. SIAM, 2025. URL: https://doi.org/10.1137/1.9781611978759.17.
  30. Alice Lasserre, Jean Marie Couteyen-Carpaye, Abdou Guermouche, and Raymond Namyst. Multi-Criteria Mesh Partitioning for an Explicit Temporal Adaptive Task-Distributed Finite-Volume Solver. In International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pages 976-985. IEEE, 2024. URL: https://doi.org/10.1109/IPDPSW63119.2024.00168.
  31. Lingxiao Ma, Zhi Yang, Youshan Miao, Jilong Xue, Ming Wu, Lidong Zhou, and Yafei Dai. NeuGraph: Parallel Deep Neural Network Computation on Large Graphs. In USENIX Annual Technical Conference (USENIX ATC), pages 443-458. USENIX Association, 2019. URL: https://www.usenix.org/conference/atc19/presentation/ma.
  32. Nikolai Maas. Benchmark Sets and Experimental Results for "High- Quality Multi-Constraint Hypergraph Partitioning via Greedy Rebalancing" , April 2026. URL: https://doi.org/10.5281/zenodo.19630135.
  33. Nikolai Maas. High-Quality Multi-Constraint Hypergraph Partitioning via Greedy Rebalancing, 2026. URL: https://doi.org/10.48550/arXiv.2605.28333.
  34. 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.
  35. 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.
  36. Kiminori Matsuzaki and Kento Emoto. Implementing Fusion-Equipped Parallel Skeletons by Expression Templates. In 21st Symposium on Implementation and Application of Functional Languages (IFL), volume 6041, pages 72-89, 2009. URL: https://doi.org/10.1007/978-3-642-16478-1_5.
  37. 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, 2024. URL: https://doi.org/10.1145/3626183.3660257.
  38. Kirk Schloegel, George Karypis, and Vipin Kumar. Parallel Multilevel Algorithms for Multi-constraint Graph Partitioning. In 6th European Conference on Parallel Processing (Euro-Par), volume 1900, pages 296-310, 2000. URL: https://doi.org/10.1007/3-540-44520-X_39.
  39. Kirk Schloegel, George Karypis, and Vipin Kumar. Graph Partitioning for Dynamic, Adaptive and Multi-phase Scientific Simulations. In International Conference on Cluster Computing (CLUSTER), pages 271-273. IEEE Computer Society, 2001. URL: https://doi.org/10.1109/CLUSTR.2001.959987.
  40. Kirk Schloegel, George Karypis, and Vipin Kumar. Parallel Static and Dynamic Multi-Constraint Graph Partitioning. Concurrency and Computation: Practice and Experience, 14(3):219-240, 2002. URL: https://doi.org/10.1002/CPE.605.
  41. Navaratnasothie Selvakkumaran, Abhishek Ranjan, Salil Raje, and George Karypis. Multi-Resource Aware Partitioning Algorithms for FPGAs with Heterogeneous Resources. In 41th Design Automation Conference (DAC), pages 741-746, 2004. URL: https://doi.org/10.1145/996566.996768.
  42. George M. Slota, Kamesh Madduri, and Sivasankaran Rajamanickam. PuLP: Scalable Multi-Objective Multi-Constraint Partitioning for Small-World Networks. In IEEE International Conference on Big Data, pages 481-490. IEEE, 2014. URL: https://doi.org/10.1109/BIGDATA.2014.7004265.
  43. David Vandevoorde and Nicolai Josuttis. C++ Templates: The Complete Guide, 2002. Google Scholar
  44. Todd Veldhuizen. Expression Templates, 1995. Google Scholar
  45. 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.
  46. Cheng Wan, Youjie Li, Cameron R. Wolfe, Anastasios Kyrillidis, Nam Sung Kim, and Yingyan Lin. PipeGCN: Efficient Full-Graph Training of Graph Convolutional Networks with Pipelined Feature Communication. In 10th International Conference on Learning Representations (ICLR). OpenReview.net, 2022. URL: https://openreview.net/forum?id=kSwqMH0zn1F.
  47. Marvin Williams, Peter Sanders, and Roman Dementiev. Engineering MultiQueues: Fast Relaxed Concurrent Priority Queues. In 29th European Symposium on Algorithms (ESA), volume 204, pages 81:1-81:17, 2021. URL: https://doi.org/10.4230/LIPIcs.ESA.2021.81.
  48. Field G. Van Zee and Robert A. van de Geijn. BLIS: A Framework for Rapidly Instantiating BLAS Functionality. ACM Transactions on Mathematical Software, 41(3):14:1-14:33, 2015. URL: https://doi.org/10.1145/2764454.
  49. 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