Skip to main content
SpringerLink
Log in
Book cover

Latin American Symposium on Theoretical Informatics

LATIN 2008: LATIN 2008: Theoretical Informatics pp 216–227Cite as

Bandwidth of Bipartite Permutation Graphs in Polynomial Time

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4957))

Abstract

We give the first polynomial-time algorithm that computes the bandwidth of bipartite permutation graphs. Prior to our work, polynomial-time algorithms for exact computation of bandwidth were known only for caterpillars of hair length 2, chain graphs, cographs, and interval graphs.

This work is supported by the Research Council of Norway through grant 166429/V30. In this extended abstract most proofs are omitted; they can be found in a technical report [12].

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Assmann, S.F., Peck, G.W., Sysło, M.M., Zak, J.: The bandwidth of caterpillars with hairs of length 1 and 2. SIAM J. Algebraic and Discrete Methods 2, 387–393 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blache, G., Karpinski, M., Wirtgen, J.: On approximation intractability of the bandwidth problem. Technical report, University of Bonn (1997)

    Google Scholar 

  3. Blum, A., Konjevod, G., Ravi, R., Vempala, S.: Semi-Definite Relaxations for Minimum Bandwidth and other Vertex-Ordering Problems. In: Proceedings of STOC 1998, pp. 100–105. ACM, New York (1998)

    Google Scholar 

  4. Bodlaender, H.L., Fellows, M.R., Hallet, M.T.: Beyond NP-completeness for problems of bounded width (extended abstract): hardness for the W hierarchy. In: Proceedings of STOC 1994, pp. 449–458. ACM, New York (1994)

    Google Scholar 

  5. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)

    Google Scholar 

  6. Feige, U.: Approximating the Bandwidth via Volume Respecting Embeddings. In: Proceedings of STOC 1998, pp. 90–99. ACM, New York (1998)

    Google Scholar 

  7. Feige, U., Talwar, K.: Approximating the Bandwidth of Caterpillars. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) APPROX 2005 and RANDOM 2005. LNCS, vol. 3624, pp. 62–73. Springer, Heidelberg (2005)

    Google Scholar 

  8. Fishburn, P., Tanenbaum, P., Trenk, A.: Linear discrepancy and bandwidth. Order 18, 237–245 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. George, J.A., Liu, J.W.H.: Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall Inc., Englewood Cliffs, New Jersey (1981)

    MATH  Google Scholar 

  10. Gupta, A.: Improved bandwidth approximation for trees. In: Proceedings of SODA 2000, pp. 788–793. ACM, SIAM (2000)

    Google Scholar 

  11. Haralambides, J., Makedon, F., Monien, B.: Bandwidth Minimization: An Approximation Algorithm for Caterpillars. Mathematical Systems Theory 24(3), 169–177 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  12. Heggernes, P., Kratsch, D., Meister, D.: Bandwidth of bipartite permutation graphs in polynomial time. In: Reports in Informatics, University of Bergen, Norway, vol. 356 (2007)

    Google Scholar 

  13. Kleitman, D.J., Vohra, R.V.: Computing the bandwidth of interval graphs. SIAM J. Disc. Math. 3, 373–375 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kloks, T., Kratsch, D., Müller, H.: Bandwidth of chain graphs. Information Processing Letters 68, 313–315 (1998)

    Article  MathSciNet  Google Scholar 

  15. Kloks, T., Kratsch, D., Müller, H.: Approximating the bandwidth for AT-free graphs. Journal of Algorithms 32, 41–57 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Meister, D.: Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs. Disc. Appl. Math. 146, 193–218 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Monien, B.: The bandwidth minimization problem with hair length 3 is NP-complete. SIAM J. Alg. Disc. Meth. 7, 505–512 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  18. Papadimitriou, C.: The NP-completeness of the bandwidth minimization problem. Computing 16, 263–270 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  19. Spinrad, J., Brandstädt, A., Stewart, L.: Bipartite permutation graphs. Disc. Appl. Math. 18, 279–292 (1987)

    Article  MATH  Google Scholar 

  20. Unger, W.: The Complexity of the Approximation of the Bandwidth Problem. In: Proceedings of FOCS 1998, pp. 82–91. IEEE, Los Alamitos (1998)

    Google Scholar 

  21. Yan, J.H.: The bandwidth problem in cographs. Tamsui Oxf. J. Math. Sci. 13, 31–36 (1997)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, PO Box 7803, N-5020, Bergen, Norway

    Pinar Heggernes & Daniel Meister

  2. Laboratoire d’Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045, Metz Cedex 01, France

    Dieter Kratsch

Authors
  1. Pinar Heggernes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dieter Kratsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Meister
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Eduardo Sany Laber Claudson Bornstein Loana Tito Nogueira Luerbio Faria

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Heggernes, P., Kratsch, D., Meister, D. (2008). Bandwidth of Bipartite Permutation Graphs in Polynomial Time. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78773-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78772-3

  • Online ISBN: 978-3-540-78773-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation