Optimal embedding of a toroidal array in a linear array

  • Heiko Schröder
  • Ondrej Sýkora
  • Imrich Vrťo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 529)


We prove that any embedding of m×n toroidal array into mn×1 linear array contains a wire of length 2min{m,n} − 2. We describe an embedding with the maximal wire length 2min{m,n} and improve this to 2n − 1 for m=n.


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  1. [1]
    Chinn, P. Z., Chvátalová, J., Dewdney, A. K., Gibbs, N. E., The bandwidth problem for graphs and matrices — a survey, Journal of Graph Theory, 6, 1982, 223–254.Google Scholar
  2. [2]
    Chung, F. R. K., Labelings of graphs, Chapter 7 in Selected Topics in Graph Theory, 3, (eds. L.Beineke and R.Wilson), Academic Press, 151–168.Google Scholar
  3. [3]
    Chvátalová, J., Optimal labeling of a product of two paths, Discrete Mathematics, 11, 1975, 249–253.Google Scholar
  4. [4]
    Chvátalová, J., Dewdney, A. K., Gibbs, N. E., Korfhage, R. R., The bandwidth problem for graphs: a collection of recent results. Res. Rep. No. 24, Department of Computer Science, UWO, London, Ontario, 1975.Google Scholar
  5. [5]
    FitzGerald, C. H., Optimal indexing of the vertices of graphs, Mathematics of Computation, 28, 127, 1974, 825–831.Google Scholar
  6. [6]
    Hoffman, A. J., Martin, M. S., Rose, D. J., Complexity bounds for regular finite difference and finite grids, SIAM J. Numerical Analysis, 10, 1973, 364–369.Google Scholar
  7. [7]
    Monien, B., Sudborough, H., Embedding one interconnection network in another, Computing Supplement., 7, 1990, 257–282.Google Scholar
  8. [8]
    Da-Lun Wang, Ping Wang, Discrete isoperimetric problems, SIAM J. Applied Mathematics, 32, 4, 1977, 860–870.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Heiko Schröder
    • 1
  • Ondrej Sýkora
    • 2
  • Imrich Vrťo
    • 2
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of NewcastleAustralia
  2. 2.Computing Centre, Slovak Academy of SciencesBratislavaCzecho-Slovakia

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