Engineering Multilevel Graph Partitioning Algorithms

  • Peter Sanders
  • Christian Schulz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from multigrid linear solvers. Local improvement algorithms are based on max-flow min-cut computations and more localized FM searches. By combining these techniques, we obtain an algorithm that is fast on the one hand and on the other hand is able to improve the best known partitioning results for many inputs. For example, in Walshaw’s well known benchmark tables we achieve 317 improvements for the tables at 1%, 3% and 5% imbalance. Moreover, in 118 out of the 295 remaining cases we have been able to reproduce the best cut in this benchmark.


Local Search Large Graph Graph Partitioning Topological Order Balance Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Andersen, R., Lang, K.J.: An algorithm for improving graph partitions. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 651–660. SIAM, Philadelphia (2008)Google Scholar
  2. 2.
    Briggs, W.L., McCormick, S.F.: A multigrid tutorial. Soc. for Ind. Mathe (2000)Google Scholar
  3. 3.
    Fjallstrom, P.O.: Algorithms for graph partitioning: A survey. Linkoping Electronic Articles in Computer and Information Science 3(10) (1998)Google Scholar
  4. 4.
    Holtgrewe, M., Sanders, P., Schulz, C.: Engineering a Scalable High Quality Graph Partitioner. In: 24th IEEE International Parallal and Distributed Processing Symposium (2010)Google Scholar
  5. 5.
    Lang, K., Rao, S.: A flow-based method for improving the expansion or conductance of graph cuts. In: Bienstock, D., Nemhauser, G.L. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 325–337. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Meyerhenke, H., Monien, B., Sauerwald, T.: A new diffusion-based multilevel algorithm for computing graph partitions of very high quality. In: IEEE International Symposium on Parallel and Distributed Processing, IPDPS 2008, pp. 1–13 (2008)Google Scholar
  7. 7.
    Osipov, V., Sanders, P.: n-Level Graph Partitioning. In: 18th European Symposium on Algorithms (2010); see also arxiv preprint arXiv:1004.4024Google Scholar
  8. 8.
    Pellegrini, F.: Scotch home page,
  9. 9.
    Picard, J.C., Queyranne, M.: On the structure of all minimum cuts in a network and applications. Mathematical Programming Studies 13, 8–16 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Sanders, P., Schulz, C.: Engineering Multilevel Graph Partitioning Algorithms. Technical report, Karlsruhe Institute of Technology (2010); see ArXiv preprint arXiv:1012.0006v3Google Scholar
  11. 11.
    Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high performance scientific simulations. In: Dongarra, J., et al. (eds.) CRPC Par. Comp. Handbook. Morgan Kaufmann, San Francisco (2000)Google Scholar
  12. 12.
    Southwell, R.V.: Stress-calculation in frameworks by the method of “Systematic relaxation of constraints”. Proc. Roy. Soc. Edinburgh Sect. A, 57–91 (1935)Google Scholar
  13. 13.
    Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131(1), 325–372 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Walshaw, C., Cross, M.: Mesh Partitioning: A Multilevel Balancing and Refinement Algorithm. SIAM Journal on Scientific Computing 22(1), 63–80 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Walshaw, C., Cross, M.: JOSTLE: Parallel Multilevel Graph-Partitioning Software – An Overview. In: Magoules, F. (ed.) Mesh Partitioning Techniques and Domain Decomposition Techniques, pp. 27–58. Civil-Comp Ltd (2007) (invited chapter)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Peter Sanders
    • 1
  • Christian Schulz
    • 1
  1. 1.Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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