Advertisement

Bisection of Random Cubic Graphs

  • J. Díaz
  • N. Do
  • M. J. Sernal
  • N. C. Wormald
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)

Abstract

We present two randomized algorithms to bound the bisection width of random n-vertex cubic graphs. We obtain an asymptotic upper bound for the bisection width of 0.174039n and a corresponding lower bound of 1.325961n. The analysis is based on the differential equation method.

Keywords

Greedy Algorithm Random Graph Hamiltonian Cycle Bipartite Subgraph Random Geometric Graph 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Achlioptas. Setting 2 variables at a time yields a new lower bound for random 3-sat. In 32nd Annual ACM Symposium on Theory of Computing (STOC 2000), pages 28–37, 2000.Google Scholar
  2. 2.
    B. Bollobas. Random Graphs. Academic Press, London, 1985.zbMATHGoogle Scholar
  3. 3.
    T. Bui, S. Chaudhuri, T. Leighton, and M. Sipser. Graph bisection algorithms with good average case behavior. Combinatorica, 7:171–191, 1987.CrossRefMathSciNetGoogle Scholar
  4. 4.
    J. Díaz, M. D. Penrose, J. Petit, and M. Serna. Approximating layout problems on random geometric graphs. Journal of Algorithms, 39:78–116, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    A. Frieze and M. R. Jerrum. Improved approximation algorithms for max k-cut and max bisection. Algorithmica, 18:61–67, 1997.CrossRefMathSciNetGoogle Scholar
  6. 6.
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979.zbMATHGoogle Scholar
  7. 7.
    M. X. Goemans and D. P. Williamson. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. J. As-soc. Comput. Mach., 42(6):1115–1145, 1995.zbMATHMathSciNetGoogle Scholar
  8. 8.
    S. Janson T. Łuczak and A. Ruciński. Random graphs. Wiley, New York, 2000.zbMATHGoogle Scholar
  9. 9.
    M. Karpinski, M. Kowaluk and A. Lingas. Approximation algorithms for max-bisection on low degree regular graphs and planar graphs. Technical report, Department of Computer Science, University of Bonn, 2000.Google Scholar
  10. 10.
    A. V. Kostochka and L. S. Melnikov. On bounds of the bisection width of cubic graphs. In J. Nesetril and M. Fiedler, editors, Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity, pages 151–154. Elsevier Science Publishers, 1992.Google Scholar
  11. 11.
    R. W. Robinson and N. C. Wormald. Almost all cubic graphs are hamiltonian. Random Structures and Algorithms, 19:128–147, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    N. C. Wormald. Differential equations for random processes and random graphs. Annals of Applied Probability, 5:1217–1235, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    N. C. Wormald. The differential equation method for random graph processes and greedy algorithms. In M. Karoński and H. Prömel, editors, Lectures on Approximation and Randomized Algorithms, pages 73–155. PWN, Warsaw, 1999.Google Scholar
  14. 14.
    N. C. Wormald. Models of random regular graphs. In Surveys in Combinatorics, pages 239–298. Cambridge University Press, 1999.Google Scholar
  15. 15.
    N. C. Wormald. Analysis of greedy algorithms on graphs with bounded degrees. Discrete Mathematics, 2002. Submitted.Google Scholar
  16. 16.
    Y. Ye. A.699-approximation algorithm for Max-Bisection. Math. Program., 90(1, Ser. A):101–111, 2001.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • J. Díaz
    • 1
  • N. Do
    • 2
  • M. J. Sernal
    • 1
  • N. C. Wormald
    • 2
  1. 1.Dept. Llenguatges i SistemesUniversitat Politecnica de CatalunyaBarcelonaSpain
  2. 2.Department of Mathematics and StatisticsUniversity of MelbourneAustralia

Personalised recommendations