On Partitioning Problems with Complex Objectives

  • Kamer Kaya
  • François-Henry Rouet
  • Bora Uçar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7155)


Hypergraph and graph partitioning tools are used to partition work for efficient parallelization of many sparse matrix computations. Most of the time, the objective function that is reduced by these tools relates to reducing the communication requirements, and the balancing constraints satisfied by these tools relate to balancing the work or memory requirements. Sometimes, the objective sought for having balance is a complex function of a partition. We mention some important class of parallel sparse matrix computations that have such balance objectives. For these cases, the current state of the art partitioning tools fall short of being adequate. To the best of our knowledge, there is only a single algorithmic framework in the literature to address such balance objectives. We propose another algorithmic framework to tackle complex objectives and experimentally investigate the proposed framework.


Hypergraph partitioning graph partitioning sparse matrix partitioning parallel sparse matrix computations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alpert, C.J., Kahng, A.B.: Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal 19, 1–81 (1995)zbMATHCrossRefGoogle Scholar
  2. 2.
    Aykanat, C., Cambazoglu, B.B., Uçar, B.: Multi-level direct k-way hypergraph partitioning with multiple constraints and fixed vertices. J. Parallel Distr. Com 68, 609–625 (2008)CrossRefGoogle Scholar
  3. 3.
    Aykanat, C., Pınar, A., Çatalyürek, Ü.V.: Permuting sparse rectangular matrices into block-diagonal form. SIAM J. Sci. Comput. 25, 1860–1879 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bisseling, R.H., Meesen, W.: Communication balancing in parallel sparse matrix-vector multiplication. ETNA 21, 47–65 (2005)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Boman, E., Devine, K., Fisk, L.A., Heaphy, R., Hendrickson, B., Vaughan, C., Catalyurek, U., Bozdag, D., Mitchell, W., Teresco, J.: Zoltan 3.0: Parallel Partitioning, Load-balancing, and Data Management Services; User’s Guide. Sandia National Laboratories, Albuquerque, NM (2007)Google Scholar
  6. 6.
    Çatalyürek, Ü.V., Aykanat, C.: PaToH: A multilevel hypergraph partitioning tool, ver. 3.0. Tech. Rep. BU-CE-9915, Bilkent Univ., Dept. Computer Eng. (1999)Google Scholar
  7. 7.
    Çatalyürek, Ü.V., Aykanat, C., Uçar, B.: On two-dimensional sparse matrix partitioning: Models, methods, and a recipe. SIAM J. Sci. Comput. 32, 656–683 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Hendrickson, B., Kolda, T.G.: Partitioning rectangular and structurally unsymmetric sparse matrices for parallel processing. SIAM J. Sci. Comput. 21, 2048–2072 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Karypis, G., Kumar, V.: MeTiS: A software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices, version 4.0. Univ. Minnesota, Dept. Comp. Sci. Eng. (1998)Google Scholar
  10. 10.
    Karypis, G., Kumar, V.: Multilevel algorithms for multi-constraint graph partitioning. Tech. Rep. 98-019, Univ. Minnesota, Dept. Comp. Sci. Eng. (1998)Google Scholar
  11. 11.
    Kaya, K., Rouet, F.H., Uçar, B.: On partitioning problems with complex objectives. Tech. Rep. RR-7546, INRIA, France (2011)Google Scholar
  12. 12.
    Lengauer, T.: Combinatorial Algorithms for Integrated Circuit Layout. Wiley–Teubner, Chichester (1990)zbMATHGoogle Scholar
  13. 13.
    Moulitsas, I., Karypis, G.: Partitioning algorithms for simultaneously balancing iterative and direct methods. Tech. Rep. 04-014, Univ. Minnesota, Dept. Comp. Sci. Eng. (2004)Google Scholar
  14. 14.
    Pellegrini, F.: SCOTCH 5.1 User’s Guide. Laboratoire Bordelais de Recherche en Informatique (LaBRI) (2008)Google Scholar
  15. 15.
    Pınar, A., Hendrickson, B.: Partitioning for complex objectives. In: IPDPS 2001, CDROM, p. 121. IEEE Computer Society, Washington, DC (2001)Google Scholar
  16. 16.
    Sanchis, L.A.: Multiple-way network partitioning with different cost functions. IEEE T. Comput. 42, 1500–1504 (1993)CrossRefGoogle Scholar
  17. 17.
    Schloegel, K., Karypis, G., Kumar, V.: Parallel Multilevel Algorithms for Multi-constraint Graph Partitioning. In: Bode, A., Ludwig, T., Karl, W.C., Wismüller, R. (eds.) Euro-Par 2000. LNCS, vol. 1900, pp. 296–310. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Uçar, B., Aykanat, C.: Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies. SIAM J. Sci. Comput. 25, 1827–1859 (2004)CrossRefGoogle Scholar
  19. 19.
    Vastenhouw, B., Bisseling, R.H.: A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. SIAM Rev. 47, 67–95 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Yamazaki, I., Li, X.S., Rouet, F.H., Uçar, B.: Combinatorial problems in a parallel hybrid linear solver. In: Becker, M., Lotz, J., Mosenkis, V., Naumann, U. (eds.) Abstracts of 5th SIAM Workshop on Combinatorial Scientific Computing. pp. 87–89. RWTH Aachen University (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kamer Kaya
    • 1
  • François-Henry Rouet
    • 2
  • Bora Uçar
    • 3
  1. 1.CERFACSToulouseFrance
  2. 2.Université de Toulouse, INPT (ENSEEIHT)-IRITFrance
  3. 3.CNRS and ENS LyonFrance

Personalised recommendations