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Multilevel Hypergraph Partitioning with Vertex Weights Revisited

Authors Tobias Heuer, Nikolai Maas, Sebastian Schlag

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Tobias Heuer
  • Karlsruhe Institute of Technology, Germany
Nikolai Maas
  • Karlsruhe Institute of Technology, Germany
Sebastian Schlag
  • Karlsruhe Institute of Technology, Germany

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Tobias Heuer, Nikolai Maas, and Sebastian Schlag. Multilevel Hypergraph Partitioning with Vertex Weights Revisited. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.SEA.2021.8

Abstract

The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications often use vertex and edge weights to accurately model the underlying problem, the HGP research community commonly works with unweighted instances. In this paper, we argue that, in the presence of vertex weights, current balance constraint definitions either yield infeasible partitioning problems or allow unnecessarily large imbalances and propose a new definition that overcomes these problems. We show that state-of-the-art hypergraph partitioners often struggle considerably with weighted instances and tight balance constraints (even with our new balance definition). Thus, we present a recursive-bipartitioning technique that is able to reliably compute balanced (and hence feasible) solutions. The proposed method balances the partition by pre-assigning a small subset of the heaviest vertices to the two blocks of each bipartition (using an algorithm originally developed for the job scheduling problem) and optimizes the actual partitioning objective on the remaining vertices. We integrate our algorithm into the multilevel hypergraph partitioner KaHyPar and show that our approach is able to compute balanced partitions of high quality on a diverse set of benchmark instances.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Hypergraphs
  • Mathematics of computing → Graph algorithms
Keywords
  • multilevel hypergraph partitioning
  • balanced partitioning
  • vertex weights

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References

  1. Y. Akhremtsev, T. Heuer, P. Sanders, and S. Schlag. Engineering a Direct k-way Hypergraph Partitioning Algorithm. In 19th Workshop on Algorithm Engineering and Experiments (ALENEX), pages 28-42. SIAM, January 2017. Google Scholar
  2. C. J. Alpert. The ISPD98 Circuit Benchmark Suite. In International Symposium on Physical Design (ISPD), pages 80-85, April 1998. Google Scholar
  3. C. J. Alpert and A. B. Kahng. Recent Directions in Netlist Partitioning: A Survey. Integration: The VLSI Journal, 19(1-2):1-81, 1995. Google Scholar
  4. C. Aykanat, B. B. Cambazoglu, and B. 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. Google Scholar
  5. D. A. Bader, H. Meyerhenke, P. Sanders, and D. Wagner, editors. Graph Partitioning and Graph Clustering, 10th DIMACS Implementation Challenge Workshop, volume 588 of Contemporary Mathematics. American Mathematical Society, February 2013. Google Scholar
  6. M. A. Bender and M. Farach-Colton. The LCA Problem Revisited. In Latin American Symposium on Theoretical Informatics, pages 88-94. Springer, 2000. Google Scholar
  7. R. H. Bisseling, B. O. Auer Fagginger, A. N. Yzelman, T. van Leeuwen, and Ü. V. Çatalyürek. Two-Dimensional Approaches to Sparse Matrix Partitioning. Combinatorial Scientific Computing, pages 321-349, 2012. Google Scholar
  8. T. N. Bui and C. Jones. Finding Good Approximate Vertex and Edge Partitions is NP-Hard. Information Processing Letters, 42(3):153-159, May 1992. Google Scholar
  9. A. E. Caldwell, A. B. Kahng, and I. L. Markov. Improved Algorithms for Hypergraph Bipartitioning. In Asia South Pacific Design Automation Conference (ASP-DAC), pages 661-666, 2000. Google Scholar
  10. A. E. Caldwell, A. B. Kahng, and I. L. Markov. Iterative Partitioning with Varying Node Weights. VLSI Design, 11(3):249-258, 2000. Google Scholar
  11. Ü. V Çatalyürek and C. Aykanat. Decomposing Irregularly Sparse Matrices for Parallel Matrix-Vector Multiplication. In International Workshop on Parallel Algorithms for Irregularly Structured Problems, pages 75-86. Springer, 1996. Google Scholar
  12. Ü. V. Çatalyürek and C. Aykanat. PaToH: Partitioning Tool for Hypergraphs. https://www.cc.gatech.edu/~umit/PaToH/manual.pdf, 2011.
  13. Ü. V. Çatalyürek 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. Google Scholar
  14. Ü. V. Çatalyürek, M. Deveci, K. Kaya, and B. Uçar. UMPa: A Multi-Objective, Multi-Level Partitioner for Communication Minimization. In Graph Partitioning and Graph Clustering, 10th DIMACS Implementation Challenge Workshop, pages 53-66, February 2012. Google Scholar
  15. T. Davis, I. S. Duff, and S. Nakov. Design and Implementation of a Parallel Markowitz Threshold Algorithm. SIAM Journal on Matrix Analysis and Applications, 41(2):573-590, April 2020. Google Scholar
  16. K. D. Devine, E. G. Boman, R. T. Heaphy, R. H. Bisseling, and Ü. V. Çatalyürek. Parallel Hypergraph Partitioning for Scientific Computing. In 20th International Parallel and Distributed Processing Symposium (IPDPS), April 2006. Google Scholar
  17. E. D. Dolan and J. J. Moré. Benchmarking Optimization Software with Performance Profiles. Mathematical Programming, 91(2):201-213, 2002. Google Scholar
  18. S. Dutt and H. Theny. Partitioning Around Roadblocks: Tackling Constraints with Intermediate Relaxations. In International Conference on Computer-Aided Design (ICCAD), pages 350-355, November 1997. Google Scholar
  19. C. M. Fiduccia and R. M. Mattheyses. A Linear-Time Heuristic for Improving Network Partitions. In 19th Conference on Design Automation (DAC), pages 175-181, 1982. Google Scholar
  20. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness, volume 174. W.H. Freeman, San Francisco, 1979. Google Scholar
  21. Lars Gottesbüren, Michael Hamann, Sebastian Schlag, and Dorothea Wagner. Advanced Flow-Based Multilevel Hypergraph Partitioning. In 18th International Symposium on Experimental Algorithms (SEA 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. Google Scholar
  22. R. L. Graham. Bounds on Multiprocessing Timing Anomalies. SIAM Journal on Applied Mathematics, 17(2):416-429, 1969. Google Scholar
  23. R. L. Graham, E. L. Lawler, J. K. Lenstra, and R. Kan. Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey. In Annals of Discrete Mathematics, volume 5, pages 287-326. Elsevier, 1979. Google Scholar
  24. S. A. Hauck. Multi-FPGA Systems. PhD thesis, University of Washington, 1995. Google Scholar
  25. T. Heuer. Engineering Initial Partitioning Algorithms for direct k-way Hypergraph Partitioning. Bachelor thesis, Karlsruhe Institute of Technology, August 2015. Google Scholar
  26. T. Heuer, P. Sanders, and S. Schlag. Network Flow-Based Refinement for Multilevel Hypergraph Partitioning. ACM Journal of Experimental Algorithmics (JEA), 24(1):2.3:1-2.3:36, September 2019. Google Scholar
  27. T. Heuer and S. Schlag. Improving Coarsening Schemes for Hypergraph Partitioning by Exploiting Community Structure. In 16th International Symposium on Experimental Algorithms (SEA), Leibniz International Proceedings in Informatics (LIPIcs), pages 21:1-21:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, June 2017. Google Scholar
  28. G. Karypis. A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices, Version 5.1.0. Technical report, University of Minnesota, 2013. Google Scholar
  29. G. Karypis, R. Aggarwal, V. Kumar, and S. Shekhar. Multilevel Hypergraph Partitioning: Application in VLSI Domain. In 34th Conference on Design Automation (DAC), pages 526-529, June 1997. Google Scholar
  30. G. Karypis and V. Kumar. Multilevel k-way Hypergraph Partitioning. VLSI Design, 11(3):285-300, 2000. Google Scholar
  31. B. W. Kernighan and S. Lin. An Efficient Heuristic Procedure for Partitioning Graphs. The Bell System Technical Journal, 49(2):291-307, February 1970. Google Scholar
  32. T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. John Wiley & Sons, Inc., 1990. Google Scholar
  33. J. Leskovec and A. Krevl. SNAP Datasets: Stanford Large Network Dataset Collection. http://snap.stanford.edu/data, 2014. Google Scholar
  34. N. Maas. Multilevel Hypergraph Partitioning with Vertex Weights Revisited. Bachelor thesis, Karlsruhe Institute of Technology, May 2020. Google Scholar
  35. D. A. Papa and I. L. Markov. Hypergraph Partitioning and Clustering. In Handbook of Approximation Algorithms and Metaheuristics. Citeseer, 2007. Google Scholar
  36. M. Pinedo. Scheduling, volume 29. Springer, 2012. Google Scholar
  37. S. Schlag, V. Henne, T. Heuer, H. Meyerhenke, P. Sanders, and C. Schulz. k-way Hypergraph Partitioning via n-Level Recursive Bisection. In 18th Workshop on Algorithm Engineering and Experiments (ALENEX), pages 53-67. SIAM, January 2016. Google Scholar
  38. Sebastian Schlag. High-Quality Hypergraph Partitioning. PhD thesis, Karlsruhe Institute of Technology, 2020. Google Scholar
  39. C. Schulz. High Quality Graph Partitioning. PhD thesis, Karlsruhe Institute of Technology, 2013. Google Scholar
  40. H. Shin and C. Kim. A Simple Yet Effective Technique for Partitioning. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 1(3):380-386, 1993. Google Scholar
  41. B. Vastenhouw and R. H. Bisseling. A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication. SIAM Review, 47(1):67-95, 2005. Google Scholar
  42. N. Viswanathan, C. J. Alpert, C. C. N. Sze, Z. Li, and Y. Wei. The DAC 2012 Routability-Driven Placement Contest and Benchmark Suite. In 49th Conference on Design Automation (DAC), pages 774-782. ACM, June 2012. Google Scholar
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