Optimal cutwidths and bisection widths of 2- and 3-dimensional meshes

  • José Rolim
  • Ondrej Sýkora
  • Imrich Vrt'o
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1017)


We prove exact cutwidths and bisection widths of ordinary, cylindrical and toroidal meshes. This answers an open problem in [9]. We also give upper bounds for cutwidths and bisection widths of many dimensional meshes. Furthemore, we show the exact cyclic cutwidth of 2-dimensional toroidal meshes and prove optimal upper and lower bounds for other meshes.


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  1. 1.
    Ahlswede, R., Bezrukov, S., Edge isoperimetric theorems for integer point arrays, Technical Report No. 94-064, University of Bielefeld, 1994.Google Scholar
  2. 2.
    Barth, D., Pellegrini, F., Raspaud, A., Roman, J., On bandwidth, cutwidth and quotient graphs, RAIRO Informatique, Théorique et Applications, to appear.Google Scholar
  3. 3.
    Bel Hala, A., Congestion optimale du plongement de l'ypercube H(n) dans la chaineP(2n), RAIRO Informatique, Théorique et Applications 27 (1993), 1–17.Google Scholar
  4. 4.
    Bollobás, B., Leader, I., Edge-isoperimetric inequalities in the grid, Combinatorica 11 (1991), 299–314.Google Scholar
  5. 5.
    Chung, F. R. K., Labelings of graphs, in: L.Beineke and R.Wilson eds., Selected Topics in Graph Theory 3, Academic Press, New York, 1988, 151–168.Google Scholar
  6. 6.
    Garey, M.R., Johnson, D.S., Stockmayer, L., Some simplified NP-complete graph problems, Theoretical Computer Science 1 (1976), 237–267.CrossRefGoogle Scholar
  7. 7.
    Harper, L. H., Optimal assignment of number to vertices, J. Soc. Ind. Appl. Math. 12 (1964) 131–135.Google Scholar
  8. 8.
    Hart, S., A note on the edges of the n-cube, Discrete Mathematics 14 (1976), 157–163.Google Scholar
  9. 9.
    Leighton, F.T., Introduction to Parallel Algorithms and Architectures, Morgan Kaufmann, 1992.Google Scholar
  10. 10.
    Lengauer, T., Upper and lower bounds for the min-cut linear arrangement of trees, SIAM J. Algebraic and Discrete Methods 3 (1982), 99–113.Google Scholar
  11. 11.
    Lindsey II, J.H., Assignment of numbers to vertices, American Mathematical Monthly 7 (1964), 508–516.Google Scholar
  12. 12.
    Lopez, A.D., Law, H.F.S., A dense gate matrix layout method for MOS VLSI, IEEE Trans. Electron. Devices 27 (1980), 1671–1675.Google Scholar
  13. 13.
    Nakano, K., Linear layout of generalized hypercubes, in: Proc. 19th Intl. Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science 790, Springer Verlag, Berlin, 1994, 364–375.Google Scholar
  14. 14.
    Nakano, K., Chen, W., Masuzawa, T., Hagihara, K., Tokura, N., Cutwidth and bisection width of hypercube graph, IEICE Transactions J73-A (1990), 856–862, (in Japanese).Google Scholar
  15. 15.
    Yannakakis, M., A polynomial algorithm for the Min Cut Linear Arrangement of trees, J. ACM 32 (1985), 950–988.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • José Rolim
    • 1
  • Ondrej Sýkora
    • 2
  • Imrich Vrt'o
    • 2
  1. 1.Centre Universitaire d'InformatiqueUniversité GenéveGenéveSwitzerland
  2. 2.Institute for InformaticsSlovak Academy of SciencesBratislavaSlovak Republic

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