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Analytical Methods for Multilevel Graph-Partitioning

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Part of the book series: Informatik aktuell ((INFORMAT))

Abstract

The multilevel strategy is widely used for graph partitioning. We discuss analytical methods for the central parts of this approach, i.e. for the graph coarsening and the local improvement.

Supported by DFG Graduate College ‘Parallel Computer Networks in Production Technique’ (Graduiertenkolleg ‘Parallele Rechnernetze in der Produktionstechnik’)

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References

  1. E.G. Arias, K. Schneider, and S. Thies. Creating virtual stakeholders for design. J. of Planning and Design, 1998.

    Google Scholar 

  2. T.N. Bui, S. Chaudhuri, F.T. Leighton, and M. Sisper. Graph bisection algorithms with good average case behaviour. Combinatorica, 7 (2): 171–191, 1987.

    Article  MathSciNet  Google Scholar 

  3. F. d’Amore, L. Becchetti, S.L. Bezrukov, A. Marchetti-Spaccamela, M. Ottaviani, R. Preis, M. Röttger, and U.-P. Schroeder. On the embedding of refinements of 2-dimensional grids. In Euro-Par’97, volume 1300 of LNCS, pages 950–957, 1997.

    Google Scholar 

  4. T. Decker and R. Diekmann. Mapping of coarse-grained applications onto workstation-clusters. In 5th Eurornicro Workshop on Parallel and Distributed Processing (PDP’97), pages 5–12. IEEE Comp. Soc. Press, 1997.

    Google Scholar 

  5. R. Diekmann, B. Monien, and R. Preis. Using helpful sets to improve graph bisections. In Hsu, editor, Interconnection Networks and Mapping and Scheduling Parallel Computations, DIMACS Series in Disc. Math., pages 57–73. 1995.

    Google Scholar 

  6. R. Diekmann, R. Preis, F. Schlimbach, and C. Walshaw. Aspect ratio for mesh partitioning. In Euro-Par’98, volume 1470 of LNCS, pages 347–351, 1998.

    Google Scholar 

  7. H.N. Gabow. Data structures for weighted matching and nearest common ancestors with linking. In SODA’90, pages 434–443, 1990.

    Google Scholar 

  8. M.R. Garey and D.S. Johnson. Computers and Intractability - A Guide to the Theory of NP-Completeness. Freemann, 1979.

    Google Scholar 

  9. B. Hendrickson and R. Leland. The chaco user’s guide: Version 2.0. Technical Report SAND94–2692, Sandia National Laboratories, Albuquerque, NM, 1994.

    Google Scholar 

  10. B. Hendrickson and R. Leland. A multilevel algorithm for partitioning graphs. In Proc. Supercomputing ‘85. ACM, 1995.

    Google Scholar 

  11. J. Hromkovic and B. Monien. The bisection problem for graphs of degree 4 (configuring transputer systems). In Buchmann, Ganzinger, and Paul, editors, Festschrift zum 60. Geburtstag von Gunter Hotz, pages 215–234. B.G. Teubner, 1992.

    Google Scholar 

  12. J. Jensch, R. Luling, and N. Sensen. A data layout strategy for parallel web servers. In EURO-PAR’98 Parallel Processing, volume 1470 of LNCS, pages 944–952, 1998.

    Chapter  Google Scholar 

  13. G. Karypis and V. Kumar. Analysis of multilevel graph partitioning. In Proc. of 7th Supercomputing Conf., 1995.

    Google Scholar 

  14. G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. on Scientific Computing,1998. to appear.

    Google Scholar 

  15. B.W. Kernighan and S. Lin. An effective heuristic procedure for partitioning graphs. The Bell Systems Technical J., pages 291–307, 1970.

    Google Scholar 

  16. B. Monien and R. Diekmann. A local graph partitioning heuristic meeting bisection bounds. In 8th SIAM Conf. on Parallel Processing for Scientific Computing, 1997.

    Google Scholar 

  17. University of Florida. Graphs. ftp://ftp.cise.ufl.edu/pub/faculty/davis/matrices.

  18. R. Ponnusamy, N. Mansour, A. Choudhary, and G.C. Fox. Graph contraction for mapping data on parallel computers. Scientific Programming, 3: 73–82, 1994.

    Google Scholar 

  19. R. Preis. Linear time 2-approximation algorithm for maximum weighted matching in general graphs. In C. Meinel and S. Tison, editors, Symposium on Theoretical Aspects of Computer Science, volume 1563 of LNCS, pages 259–269, 1999.

    Google Scholar 

  20. R. Preis and R. Diekmann. PARTY–A software library for graph partitioning. In B.H.V. Topping, editor, Advances in Computational Mechanics with Parallel and Distributed Processing, pages 63–71, 1997.

    Google Scholar 

  21. J. Schulze, R. Diekmann, and R. Preis. Comparing nested dissection orderings for parallel sparse matrix factorization. In PDPTA ‘85, pages 280–289, 1995.

    Google Scholar 

  22. C. Walshaw, M. Cross, and M.G. Everett. A localised algorithm for optimising unstructured mesh partitions. Int. J. Supercomputer Appl., 9 (4): 280–295, 1995.

    Article  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Preis, R. (1999). Analytical Methods for Multilevel Graph-Partitioning. In: Beiersdörfer, K., Engels, G., Schäfer, W. (eds) Informatik’99. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01069-3_33

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  • DOI: https://doi.org/10.1007/978-3-662-01069-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66450-5

  • Online ISBN: 978-3-662-01069-3

  • eBook Packages: Springer Book Archive

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