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Aggregative Coarsening for Multilevel Hypergraph Partitioning

Authors Ruslan Shaydulin , Ilya Safro

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Author Details

Ruslan Shaydulin
  • School of Computing, Clemson University, Clemson, SC
Ilya Safro
  • School of Computing, Clemson University, Clemson, SC

Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1522751.

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Ruslan Shaydulin and Ilya Safro. Aggregative Coarsening for Multilevel Hypergraph Partitioning. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.SEA.2018.2

Abstract

Algorithms for many hypergraph problems, including partitioning, utilize multilevel frameworks to achieve a good trade-off between the performance and the quality of results. In this paper we introduce two novel aggregative coarsening schemes and incorporate them within state-of-the-art hypergraph partitioner Zoltan. Our coarsening schemes are inspired by the algebraic multigrid and stable matching approaches. We demonstrate the effectiveness of the developed schemes as a part of multilevel hypergraph partitioning framework on a wide range of problems.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Hypergraphs
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Matchings and factors
Keywords
  • hypergraph partitioning
  • multilevel algorithms
  • coarsening
  • matching
  • combinatorial scientific computing

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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 and Experiments, (ALENEX 2017), pages 28-42, 2017. Google Scholar
  2. Charles J Alpert and Andrew B Kahng. Recent directions in netlist partitioning: a survey. Integration, the VLSI journal, 19(1-2):1-81, 1995. Google Scholar
  3. David A Bader, Henning Meyerhenke, Peter Sanders, and Dorothea Wagner. Graph partitioning and graph clustering: 10th dimacs implementation challenge, vol. 588. American Mathematical Society, 7:210-223, 2013. Google Scholar
  4. Stephen T Barnard and Horst D Simon. Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Concurrency and computation: Practice and Experience, 6(2):101-117, 1994. Google Scholar
  5. V. D. Blondel, J.-L. Guillaume, R. Lambiotte, and R. Lefebvre. Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 10:P10008, 2008. Google Scholar
  6. Achi Brandt and Dorit Ron. Multigrid solvers and multilevel optimization strategies. In Multilevel optimization in VLSICAD, pages 1-69. Springer, 2003. Google Scholar
  7. Aydin Buluç and Erik G Boman. Towards scalable parallel hypergraph partitioning. CSRI Summer Proceedings 2008, page 109, 2008. Google Scholar
  8. Aydin Buluc, Henning Meyerhenke, Ilya Safro, Peter Sanders, and Christian Schulz. Recent advances in graph partitioning. In Algorithm Engineering: Selected Results and Surveys, volume 9220, pages 117-158. Springer, 2016. Google Scholar
  9. Ümit Çatalyürek and Cevdet Aykanat. Patoh (partitioning tool for hypergraphs). In Encyclopedia of Parallel Computing, pages 1479-1487. Springer, 2011. Google Scholar
  10. Umit V Catalyurek and Cevdet Aykanat. Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication. IEEE Trans. Parallel Distrib. Syst., 10(7):673-693, 1999. Google Scholar
  11. Umit V Catalyurek, Erik G Boman, Karen D Devine, Doruk Bozdağ, Robert T Heaphy, and Lee Ann Riesen. A repartitioning hypergraph model for dynamic load balancing. J. Parallel Distrib. Comput., 69(8):711-724, 2009. Google Scholar
  12. Jie Chen and Ilya Safro. Algebraic distance on graphs. SIAM J. Sci. Comput., 33(6):3468-3490, 2011. Google Scholar
  13. Carlo Curino, Evan Jones, Yang Zhang, and Sam Madden. Schism: a workload-driven approach to database replication and partitioning. Proceedings of the VLDB Endowment, 3(1-2):48-57, 2010. Google Scholar
  14. Timothy A Davis and Yifan Hu. The university of florida sparse matrix collection. ACM Transactions on Mathematical Software (TOMS), 38(1):1, 2011. Google Scholar
  15. Karen D Devine, Erik G Boman, Robert T Heaphy, Rob H Bisseling, and Umit V Catalyurek. Parallel hypergraph partitioning for scientific computing. In Parallel and Distributed Processing Symposium, 2006. IPDPS 2006. 20th International, pages 10-pp. IEEE, 2006. Google Scholar
  16. Karen D Devine, Erik G Boman, Robert T Heaphy, Bruce A Hendrickson, James D Teresco, Jamal Faik, Joseph E Flaherty, and Luis G Gervasio. New challenges in dynamic load balancing. Applied Numerical Mathematics, 52(2-3):133-152, 2005. Google Scholar
  17. Karen D Devine, Vitus Leung, Erik G Boman, Sivasankaran Rajamanickam, Lee Ann Riesen, and Umit Catalyurek. Zoltan user’s guide, version 3.8.(2014), 2014. URL: http://www.cs.sandia.gov/zoltan/ug_html/ug_alg_patoh.html.
  18. Charles M Fiduccia and Robert M Mattheyses. A linear-time heuristic for improving network partitions. In Papers on Twenty-five years of electronic design automation, pages 241-247. ACM, 1988. Google Scholar
  19. David Gale and Lloyd S Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9-15, 1962. Google Scholar
  20. Michael R Garey and David S Johnson. Computers and intractability, volume 29. New York, 2002. Google Scholar
  21. Mirco Gelain, Maria Silvia Pini, Francesca Rossi, K Brent Venable, and Toby Walsh. Local search approaches in stable matching problems. Algorithms, 6(4):591-617, 2013. Google Scholar
  22. Giorgos Georgiadis and Marina Papatriantafilou. Overlays with preferences: Distributed, adaptive approximation algorithms for matching with preference lists. Algorithms, 6(4):824-856, 2013. Google Scholar
  23. Dan Gusfield and Robert W Irving. The stable marriage problem: structure and algorithms. MIT press, 1989. Google Scholar
  24. Bruce Hendrickson and Robert W Leland. A multi-level algorithm for partitioning graphs. SC, 95(28), 1995. Google Scholar
  25. Van Emden Henson and Ulrike Meier Yang. Boomeramg: a parallel algebraic multigrid solver and preconditioner. Applied Numerical Mathematics, 41(1):155-177, 2002. Google Scholar
  26. Michael A Heroux, Roscoe A Bartlett, Vicki E Howle, Robert J Hoekstra, Jonathan J Hu, Tamara G Kolda, Richard B Lehoucq, Kevin R Long, Roger P Pawlowski, Eric T Phipps, et al. An overview of the trilinos project. ACM Trans. Math. Software, 31(3):397-423, 2005. Google Scholar
  27. Y. F. Hu and J. A. Scott. A multilevel algorithm for wavefront reduction. SIAM J. Sci. Comput., 23(4):1352-1375, 2001. URL: http://dx.doi.org/10.1137/S1064827500377733.
  28. Ruoming Jin, Yang Xiang, David Fuhry, and Feodor F. Dragan. Overlapping matrix pattern visualization: A hypergraph approach. Data Mining, IEEE International Conference on, 0:313-322, 2008. URL: http://dx.doi.org/10.1109/ICDM.2008.102.
  29. Emmanuel John and Ilya Safro. Single-and multi-level network sparsification by algebraic distance. Journal of Complex Networks, 5(3):352-388, 2016. Google Scholar
  30. George Karypis, Rajat Aggarwal, Vipin Kumar, and Shashi Shekhar. Multilevel hypergraph partitioning: applications in vlsi domain. IEEE Trans. Very Large Scale Integr. (VLSI) Syst., 7(1):69-79, 1999. Google Scholar
  31. George Karypis and Vipin Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput., 20(1):359-392, 1998. Google Scholar
  32. Brian W Kernighan and Shen Lin. An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J., 49(2):291-307, 1970. Google Scholar
  33. K Ashwin Kumar, Abdul Quamar, Amol Deshpande, and Samir Khuller. Sword: workload-aware data placement and replica selection for cloud data management systems. The VLDB Journal, 23(6):845-870, 2014. Google Scholar
  34. Oren E Livne and Achi Brandt. Lean algebraic multigrid (lamg): Fast graph laplacian linear solver. SIAM Journal on Scientific Computing, 34(4):B499-B522, 2012. Google Scholar
  35. Enyue Lu and SQ Zheng. A parallel iterative improvement stable matching algorithm. In International Conference on High-Performance Computing, pages 55-65. Springer, 2003. Google Scholar
  36. Fredrik Manne, Md. Naim, Håkon Lerring, and Mahantesh Halappanavar. On Stable Marriages and Greedy Matchings, pages 92-101. SIAM, 2016. URL: http://dx.doi.org/10.1137/1.9781611974690.ch10.
  37. Danny Munera, Daniel Diaz, Salvador Abreu, and Philippe Codognet. A parametric framework for cooperative parallel local search. In European Conference on Evolutionary Computation in Combinatorial Optimization, pages 13-24. Springer, 2014. Google Scholar
  38. Danny Munera, Daniel Diaz, Salvador Abreu, Francesca Rossi, Vijay A Saraswat, and Philippe Codognet. Solving hard stable matching problems via local search and cooperative parallelization. In AAAI, pages 1212-1218, 2015. Google Scholar
  39. David A Papa and Igor L Markov. Hypergraph partitioning and clustering., 2007. Google Scholar
  40. Jongsoo Park, Mikhail Smelyanskiy, Ulrike Meier Yang, Dheevatsa Mudigere, and Pradeep Dubey. High-performance algebraic multigrid solver optimized for multi-core based distributed parallel systems. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, page 54. ACM, 2015. Google Scholar
  41. Dorit Ron, Ilya Safro, and Achi Brandt. Relaxation-based coarsening and multiscale graph organization. Multiscale Modeling &Simulation, 9(1):407-423, 2011. Google Scholar
  42. Randolf Rotta and Andreas Noack. Multilevel local search algorithms for modularity clustering. Journal of Experimental Algorithmics (JEA), 16:2-3, 2011. Google Scholar
  43. I. Safro, D. Ron, and A. Brandt. Graph minimum linear arrangement by multilevel weighted edge contractions. Journal of Algorithms, 60(1):24-41, 2006. Google Scholar
  44. I. Safro, D. Ron, and A. Brandt. Multilevel algorithm for the minimum 2-sum problem. Journal of Graph Algorithms and Applications, 10(2):237-258, 2006. Google Scholar
  45. Ilya Safro, Dorit Ron, and Achi Brandt. Graph minimum linear arrangement by multilevel weighted edge contractions. Journal of Algorithms, 60(1):24-41, 2006. Google Scholar
  46. Ilya Safro, Dorit Ron, and Achi Brandt. Multilevel algorithms for linear ordering problems. ACM Journal of Experimental Algorithmics, 13, 2008. URL: http://dx.doi.org/10.1145/1412228.1412232.
  47. Ilya Safro, Peter Sanders, and Christian Schulz. Advanced coarsening schemes for graph partitioning. ACM Journal of Experimental Algorithmics (JEA), 19:2-2, 2015. Google Scholar
  48. Ilya Safro and Boris Temkin. Multiscale approach for the network compression-friendly ordering. J. Discrete Algorithms, 9(2):190-202, 2011. URL: http://dx.doi.org/10.1016/j.jda.2010.09.007.
  49. 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 and Experiments, (ALENEX 2016), pages 53-67, 2016. Google Scholar
  50. Ruslan Shaydulin, Jie Chen, and Ilya Safro. Relaxation-based coarsening for multilevel hypergraph partitioning. arXiv preprint arXiv:1710.06552, 2017. Google Scholar
  51. Ruslan Shaydulin and Ilya Safro. Aggregative coarsening for multilevel hypergraph partitioning. CoRR, abs/1802.09610, 2018. URL: http://arxiv.org/abs/1802.09610.
  52. Aleksandar Trifunovic. Parallel algorithms for hypergraph partitioning. PhD thesis, University of London, 2006. Google Scholar
  53. C. Walshaw. Multilevel refinement for combinatorial optimisation problems. Annals Oper. Res., 131:325-372, 2004. Google Scholar
  54. Chris Walshaw. A multilevel approach to the travelling salesman problem. Operations Research, 50(5):862-877, 2002. Google Scholar
  55. Dengyong Zhou, Jiayuan Huang, and Bernhard Schölkopf. Learning with hypergraphs: Clustering, classification, and embedding. In NIPS, volume 19, pages 1633-1640, 2006. Google Scholar
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