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Scandinavian Workshop on Algorithm Theory

SWAT 2000: Algorithm Theory - SWAT 2000 pp 10–19Cite as

Coping with the NP-Hardness of the Graph Bandwidth Problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

Abstract.

We review several approaches of coping with NP-hardness, and see how they apply (if at all) to the problem of computing the bandwidth of a graph.

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References

  1. L. Adleman. “Algorithmic Number Theory-The Complexity Contribution”. Proc. of 35th FOCS, 1994, 88–113.

    Google Scholar 

  2. S. Assman, G. Peck, M. Syslo, J Zak. “The bandwidth of caterpillars with hairs of length 1 and 2”. SIAM J. Algebraic Discrete Methods 2 (1981), 387–393.

    Article  MathSciNet  Google Scholar 

  3. G. Blache, M. Karpinski, J. Wirtgen. “On approximation intractability of the bandwidth problem”. Manuscript, 1998.

    Google Scholar 

  4. A. Blum, G. Konjevod, R. Ravi, S. Vempala. “Semidefinite relaxations for minimum bandwidth and other vertex-ordering problems”. Proc. of 30th STOC, 1998, 100–105.

    Google Scholar 

  5. A. Blum, J. Spencer. “Coloring Random and Semi-Random k-Colorable Graphs”. Journal of Algorithms 19, 204–234, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Bodlaender, M. Fellows, M. Hallet. “Beyond NP-completeness for problems of bounded width: hardness for the W Hierarchy”. Proc. of 26th STOC, 1994, 449–458.

    Google Scholar 

  7. P. Chinn, J. Chvatalova, A. Dewdney, N. Gibbs. “The bandwidth problem for graphs and matrices-a survey”. Journal of Graph Theory, 6 (1982), 223–254.

    Article  MATH  MathSciNet  Google Scholar 

  8. F. Chung, P. Seymour. “Graphs with small bandwidth and cutwidth”. Discrete Mathematics75 (1989) 113–119.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Chvatalova. On the bandwidth problem for graphs, Ph.D. dissertation, University of Waterloo, 1980.

    Google Scholar 

  10. E. Cuthill, J. McKee. “Reducing the bandwidth of sparse symmetric matrices”. A CM National Conference Proceedings, 24, 1969, 157–172.

    Google Scholar 

  11. R. Downey, M. Fellows. Parameterized Complexity. Sringer-Verlag New York, 1999.

    Google Scholar 

  12. U. Feige. “Approximating the Bandwidth via Volume Respecting Embeddings”. Journal of Computer and System Sciences, to appear. (A preliminary version appeared in the proceedings of the 30th STOC, 1998, 90–99.)

    Google Scholar 

  13. U. Feige, J. Kilian. “On limited versus polynomial nondeterminism”. Chicago Journal of Theoretical Computer Science, 12 March 1997. http://www.cs.uchicago.edu/pub/publications/cjtcs/index.html

  14. U. Feige, J. Kilian. “Heuristics for semirandom graph problems” Journal of Computer and System Sciences, to appear. (Preliminary version in Proc. of 39th FOCS, 1998, 674–683)

    Google Scholar 

  15. U. Feige, J. Kilian. “Exponential time algorithms for computing the bandwidth of a graph”. Manuscript in preparation.

    Google Scholar 

  16. U. Feige, R. Krauthgamer. “Improved performance guarantees for bandwidth minimization heuristics”. Manuscript, 1998.

    Google Scholar 

  17. M. Garey, R. Graham, D. Johnson, D. Knuth. “Complexity results for bandwidth minimization”. SIAM J. Appl. Math. 34 (1978), 477–495.

    Article  MATH  MathSciNet  Google Scholar 

  18. O. Goldreich. “Notes on Levin’s Theory of Average-Case Complexity”. Manuscript, 1997. http://www.wisdom.weizmann.ac.il/home/odedg

  19. A. Gupta. “Improved bandwidth approximation algorithms for trees”. Proc. SODA 2000.

    Google Scholar 

  20. E. Gurari, I. Sudborough. “Improved dynamic programming algorithms for bandwidth minimization and the min-cut linear arrangement problems”. J. Algorithms, 5 (1984), 531–546.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. Haralambides, F. Makedon, B. Monien. “Bandwidth minimization: an approximation algorithm for caterpillars”. Math Systems Theory 24, 169–177 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  22. R. Impagliazzo, R. Paturi. “Complexity of k-S AT”. Proc. Computational Complexity, 1999.

    Google Scholar 

  23. R. Impagliazzo, R. Paturi, F. Zane. “Which problems have strongly exponential complexity”. Proc. FOCS 1988, 653–663.

    Google Scholar 

  24. M. Karpinski, J. Wirtgen, A. Zelikovsky. “An approximation algorithm for the bandwidth problem on dense graphs”. ECCC TR97-017.

    Google Scholar 

  25. D. Kleitman, R. Vohra. “Computing the bandwidth of interval graphs”. SIAM J. Discrete Math., 3 (1990), 373–375.

    Article  MATH  MathSciNet  Google Scholar 

  26. T. Kloks, D. Kratsch, H. Muller. “Approximating the bandwidth for asteroidal triple-free graphs”. In Algorithms-ESA’ 95, Paul Spirakis (Ed.), Lecture Notes in Computer Science 979, 434–447, Springer.

    Google Scholar 

  27. L. Levin. “Average case complete problems”. SIAM J. Comput, 15(1):285–286, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  28. B. Monien. “The bandwidth-minimization problem for caterpillars with hair-length 3 is NP-complete”. SIAM J. Algebraic Discrete Methods 7 (1986), 505–512.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  30. J. Saxe. “Dynamic programming algorithms for recognizing small-bandwidth graphs in polynomial time”. SIAM Journal on Algebraic Methods 1 (1980), 363–369.

    Google Scholar 

  31. J. Turner. “On the probable performance of heuristics for bandwidth minimization”. SIAM J. Comput., 15, (1986), 561–580.

    Article  MATH  MathSciNet  Google Scholar 

  32. W. Unger. “The complexity of the approximation of the bandwidth problem”. In Proc. 39th Annual IEEE Symposium on Foundations of Computer Science, 1998, 82–91.

    Google Scholar 

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Authors and Affiliations

  1. Weizmann Institute, Rehovot, 76100, Israel

    Uriel Feige

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  1. Uriel Feige
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© 2000 Springer-Verlag Berlin Heidelberg

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Feige, U. (2000). Coping with the NP-Hardness of the Graph Bandwidth Problem. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_2

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  • DOI: https://doi.org/10.1007/3-540-44985-X_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

  • eBook Packages: Springer Book Archive

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