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Comparison of Coarsening Schemes for Multilevel Graph Partitioning

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Learning and Intelligent Optimization (LION 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5851))

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Abstract

Graph partitioning is a well-known optimization problem of great interest in theoretical and applied studies. Since the 1990s, many multilevel schemes have been introduced as a practical tool to solve this problem. A multilevel algorithm may be viewed as a process of graph topology learning at different scales in order to generate a better approximation for any approximation method incorporated at the uncoarsening stage in the framework. In this work we compare two multilevel frameworks based on the geometric and the algebraic multigrid schemes for the partitioning problem.

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References

  1. Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete graph problems. Theoretical Computer Science 1, 237–267 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Pothen, A., Simon, H.D., Liou, K.P.: Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal of Matrix Analysis 11(3), 430–452 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. BELL System Technical Journal, 291–307 (1970)

    Google Scholar 

  4. Fiduccia, C.M., Mattheyses, R.M.: A linear-time heuristic for improving network partitions. In: Proceedings of the 19th Design Automation Conference, pp. 175–181. IEEE, Los Alamitos (1982)

    Google Scholar 

  5. Bui, T.N., Moon, B.R.: Genetic algorithm and graph partitioning. IEEE Trans. Comput. 45(7), 841–855 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Brandt, A., Ron, D.: Ch. 1: Multigrid solvers and multilevel optimization strategies. In: Cong, J., Shinnerl, J.R. (eds.) Multilevel Optimization and VLSICAD. Kluwer, Dordrecht (2003)

    Google Scholar 

  7. Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Annals Oper. Res. 131, 325–372 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chan, T.F., Cong, J., Romesis, M., Shinnerl, J.R., Sze, K., Xie, M.: mpl6: a robust multilevel mixed-size placement engine. In: Groeneveld, P., Scheffer, L. (eds.) ISPD, pp. 227–229. ACM, New York (2005)

    Google Scholar 

  9. Chang, C., Cong, J., Pan, D., Yuan, X.: Multilevel global placement with congestion control. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 22, 395–409 (2003)

    Article  Google Scholar 

  10. Cong, J., Shinnerl, J.R. (eds.): Multilevel Optimization and VLSICAD. Kluwer, Dordrecht (2003)

    Google Scholar 

  11. Safro, I., Ron, D., Brandt, A.: Multilevel algorithms for linear ordering problems. Journal of Experimental Algorithmics 13, 1.4–1.20 (2008)

    Google Scholar 

  12. Abou-Rjeili, A., Karypis, G.: Multilevel algorithms for partitioning power-law graphs. In: IPDPS (2006)

    Google Scholar 

  13. Alpert, C.J., Huang, J.H., Kahng, A.B.: Multilevel circuit partitioning. In: Design Automation Conference, pp. 530–533 (1997)

    Google Scholar 

  14. Banos, R., Gil, C., Ortega, J., Montoya, F.: Multilevel heuristic algorithm for graph partitioning. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 143–153. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Ron, D., Wishko-Stern, S., Brandt, A.: An algebraic multigrid based algorithm for bisectioning general graphs. Technical Report MCS05-01, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science (2005)

    Google Scholar 

  16. Barnard, S.T., Simon, H.D.: A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Concurrency: Practice and Experience 6, 101–107 (1994)

    Article  Google Scholar 

  17. Hendrickson, B., Leland, R.W.: A multi-level algorithm for partitioning graphs. In: Supercomputing (1995)

    Google Scholar 

  18. Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. Technical Report 95-035, University of Minnesota (1995)

    Google Scholar 

  19. Catalyurek, U., Aykanat, C.: Decomposing irregularly sparse matrices for parallel matrix-vector multiplications. In: Saad, Y., Yang, T., Ferreira, A., Rolim, J.D.P. (eds.) IRREGULAR 1996. LNCS, vol. 1117, pp. 75–86. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  20. Devine, K., Boman, E., Heaphy, R., Hendrickson, B., Vaughan, C.: Zoltan data management services for parallel dynamic applications. Computing in Science and Engineering 4(2), 90–97 (2002)

    Article  Google Scholar 

  21. Walshaw, C.: A multilevel approach to the travelling salesman problem. Tech. Rep. 00/IM/63, Comp. Math. Sci., Univ. Greenwich, London SE10 9LS, UK (2000)

    Google Scholar 

  22. Hu, Y.F., Scott, J.A.: A multilevel algorithm for wavefront reduction. SIAM J. Scientific Computing 23, 2000–2031 (2001)

    Article  MathSciNet  Google Scholar 

  23. Meyerhenke, H., Monien, B., Sauerwald, T.: A new diffusion-based multilevel algorithm for computing graph partitions of very high quality. In: Proc. 22nd International Parallel and Distributed Processing Symposium (IPDPS 2008). IEEE Computer Society, Los Alamitos (2008); Best Algorithms Paper Award

    Google Scholar 

  24. scotch: Static mapping, graph partitioning, and sparse matrix block ordering package, http://www.labri.fr/~pelegrin/scotch/

  25. Simon, H.D., Teng, S.H.: How good is recursive bisection. SIAM J. Sci. Comput. 18, 1436–1445 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  26. Brandt, A.: General highly accurate algebraic coarsening. Electronic Trans. Num. Anal. 10(2000), 1–20 (2000)

    MATH  MathSciNet  Google Scholar 

  27. Safro, I., Ron, D., Brandt, A.: Graph minimum linear arrangement by multilevel weighted edge contractions. Journal of Algorithms 60(1), 24–41 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  28. Hager, W.W., Krylyuk, Y.: Graph partitioning and continuous quadratic programming. SIAM J. Discret. Math. 12(4), 500–523 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  29. Henson, V.E., Yang, U.M.: Boomeramg: a parallel algebraic multigrid solver and preconditioner. Appl. Numer. Math. 41(1), 155–177 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  30. Gee, M., Siefert, C., Hu, J., Tuminaro, R., Sala, M.: ML 5.0 smoothed aggregation user’s guide. Technical Report SAND2006-2649, Sandia National Laboratories (2006)

    Google Scholar 

  31. Chevalier, C., Pellegrini, F.: Improvement of the efficiency of genetic algorithms for scalable parallel graph partitioning in a multi-level framework. In: Nagel, W.E., Walter, W.V., Lehner, W. (eds.) Euro-Par 2006. LNCS, vol. 4128, pp. 243–252. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  32. Chevalier, C., Pellegrini, F.: Pt-scotch: A tool for efficient parallel graph ordering. Parallel Comput. 34(6-8), 318–331 (2008)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, USA

    Cédric Chevalier

  2. Argonne National Laboratory, Argonne, IL, USA

    Ilya Safro

Authors
  1. Cédric Chevalier
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  2. Ilya Safro
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Editor information

Editors and Affiliations

  1. IRIDIA, CoDE, Université Libre de Bruxelles, Avenue F. Roosevelt 50, CP 194/6, 1050, Brussels, Belgium

    Thomas Stützle

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Chevalier, C., Safro, I. (2009). Comparison of Coarsening Schemes for Multilevel Graph Partitioning. In: Stützle, T. (eds) Learning and Intelligent Optimization. LION 2009. Lecture Notes in Computer Science, vol 5851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11169-3_14

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  • DOI: https://doi.org/10.1007/978-3-642-11169-3_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11168-6

  • Online ISBN: 978-3-642-11169-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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