Bandwidth of Split and Circular Permutation Graphs

  • Ton Kloks
  • Dieter Kratsch
  • Yvan Le Borgne
  • Haiko Müller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1928)


The BANDWIDTH minimization problem on graphs of some special graph classes is studied and the following results are obtained. The problem remains NP-complete when restricted to splitgraphs. There is a linear time algorithm to compute the exact bandwidth of a subclass of splitgraphs called hedgehogs. There is an efficient algorithm to approximate the bandwidth of circular permutation graphs within a factor of four.


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  1. 1.
    Assmann, S. F., G. W. Peck, M. M. Sys lo and J. Zak, The bandwidth of caterpillars with hairs of length 1 and 2, SIAM J. Algebraic Discrete Methods 2 (1981), pp. 387–393.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Blum, A., G. Konjevod, R. Ravi and S. Vempala, Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems, Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing (Dallas, TX, 1998), pp. 111–105.Google Scholar
  3. 3.
    Chinn, P. Z., J. Chvátalová, A. K. Dewdney and N. E. Gibbs, The bandwidthproblem for graphs and matrices-a survey, Journal of Graph Theory 6(1982), pp. 223–254.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chung, F. R. K., Labelings of graphs, Selected topics in graph theory 3 (1988), pp. 151–168.Google Scholar
  5. 5.
    Downey, R. G. and M. R. Fellows, Parameterized complexity, Springer-Verlag New York, 1998.MATHGoogle Scholar
  6. 6.
    Feige, U., Approximating the bandwidth via volume respecting embeddings, Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing(Dallas, TX, 1998).Google Scholar
  7. 7.
    Garey, M. R., R. L. Graham, D. S. Johnson and D. E. Knuth, Complexity results for bandwidth minimization, SIAM Journal on Applied Mathematics 34 (1978), pp. 477–495.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gurari, E. M. and I. H. Sudborough, Improved dynamic programming algorithms for bandwidth minimization and the MinCut linear arrangement problem, J. Algorithms 5 (1984), pp. 531–546.Google Scholar
  9. 9.
    Haralambides, J. and F. Makedon, Approximation algorithms for the bandwidth minimization problem for a large class of trees, Theory Comput. Syst. 30 (1997), pp. 67–90.MATHMathSciNetGoogle Scholar
  10. 10.
    Haralambides, J., F. Makedon and F. and B. Monien, Bandwidth minimization: An approximation algorithm for caterpillars, Math. Syst. Theory 24 (1991), pp. 169–177.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kleitman, D. J. and R.V. Vohra, Computing the bandwidth of interval graphs, SIAM Journal on Discrete Mathematics 3 (1990), pp. 373–375.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kratsch, D., P. Damaschke and A. Lubiw, Dominating cliques in chordal graphs, Discrete Mathematics 128 (1994), pp. 269–276.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kloks, T., D. Kratsch and H. Müller, Approximating the bandwidth for asteroidal triple-free graphs, Journal of Algorithms 32 (1999), pp. 41–57.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kloks, T., D. Kratsch, and H. Müller, Bandwidth of chain graphs, Information Processing Letters 68 (1998), pp. 313–315.CrossRefMathSciNetGoogle Scholar
  15. 15.
    Kratsch, D. and L. Stewart, Approximating bandwidth by mixing layouts of interval graphs, Proceedings of STACS’99, LNCS 1563, pp. 248–258.Google Scholar
  16. 16.
    Monien, B., The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete, SIAM Journal on Algebraic and Discrete Methods 7 (1986), pp. 505–512.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Rotem, D. and J. Urrutia, Circular permutation graphs, Networks 12 (1982), pp. 429–437.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Papadimitriou, C. H., The NP-completeness of the bandwidth minimization problem, Computing 16 (1976), pp. 263–270.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Parra, A., structural and algorithmic aspects of chordal graph embeddings, PhD-thesis, Technische Universität Berlin, 1996.Google Scholar
  20. 20.
    Peck, G. W. and Aditya Shastri, Bandwidth of theta graphs with short paths, Discrete Mathematics 103 (1992), pp. 177–187.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Sprague, A. P., An O(n log n) algorithm for bandwidth of interval graphs, SIAM Journal on Discrete Mathematics 7 (1994), pp. 213–220.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Unger, W., The complexity of the approximation of the bandwidth problem, Proceedings of the 39th Annual Symposium on Foundations of Computer Science (Palo Alto, California, 1998), pp. 82–91.Google Scholar
  23. 23.
    Venkatesan, G., U. Rotics, M. S. Madanlal, J. A. Makowsky, and C. Pandu Rangan, Restrictions of minimum spanner problems, Information and Computation 136 (1997), pp. 143–164.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Ton Kloks
    • 1
  • Dieter Kratsch
    • 2
  • Yvan Le Borgne
    • 3
  • Haiko Müller
    • 4
  1. 1.Department of Mathematics and Computer ScienceVrije Universiteit AmsterdamThe Netherlands
  2. 2.Laboratoire d’Informatique Théorique et AppliquéeUniversité de MetzFrance
  3. 3.Laboratoire Bordelais de Recherche en InformatiqueTalence CedexFrance
  4. 4.Fakultät für Mathematik und InformatikFriedrich-Schiller-Universität JenaJenaGermany

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