On three-dimensional layout of interconnection networks

Extended abstract
  • Tiziana Calamoneri
  • Annalisa Massini
Drawings in the Air
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

In this paper we deal with the layout of interconnection networks on three-dimensional grids. In particular, in the first part we prove a general formula for calculating an exact value for the lower bound on the volume. Then we introduce the new notion of k-3D double channel routing and we use it to exhibit an optimal three-dimensional layout for butterfly networks. Finally, we show a method to lay out multigrid and X-tree networks in optimal volume.

References

  1. 1.
    AVIOR,A.—CALAMONERI,T.—EVEN, S.—LITMAN,A.—ROSENBERG,A.L.: A Tight Layout of the Butterfly Network. Proc. ACM SPAR `96, ACM Press Ed., 1996, pp 170–175.Google Scholar
  2. 2.
    BIEDL,T.: New Lower Bounds for Orthogonal Graph Drawings. Proc.GD `95, LNCS 1027, Springer-Verlag, 1995, pp 28–39.Google Scholar
  3. 3.
    CALAMONERI,T.—STERBINI,A.: Drawing 2-, 3-and 4-colorable Graphs in O(n 2) volume. Proc. GD `96, LNCS 1190, Springer-Verlag, 1996, pp 53–62.Google Scholar
  4. 4.
    COHEN,R.F.—EADES,P.—LIN,T.—RUSKEY,F.: Three-dimensional graph drawing. Proc. GD `94, LNCS 894, Springer-Verlag, 1994, pp 1–11. Also in Algorithmica 17(2), pp 199–208, 1997.Google Scholar
  5. 5.
    FADES, P.—FENG, Q.W.: Multilevel Visualization of Clustered Graphs. Proc. GD `96, LNCS 1190, Springer-Verlag, 1996, pp 101–112.Google Scholar
  6. 6.
    FADES,P.—SYMVONIS,A.—WHITESIDES,S.: Two Algorithms for Three Dimensional Orthogonal Graph Drawing. Proc. GD `96, LNCS 1190, Springer-Verlag, 1996, pp 139–154.Google Scholar
  7. 7.
    EVEN, S.—LITMAN, A.: Layered Cross Product — A Technique to Construct Interconnection Networks. ACM SPAA `92, ACM Press Ed., 60–69, 1992.Google Scholar
  8. 8.
    LEIGHTON, F.T.: Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks. MIT Press, Cambridge, Mass, 1983.Google Scholar
  9. 9.
    MEHLORN, K.—PREPARATA, F.P.—SARRAFZADEH, M.: Channel routing in knock-knee mode: simplified algorithms and proofs. Algorithmica l, 213–221, 1986.CrossRefGoogle Scholar
  10. 10.
    PACH, J.—TÓTH, G.: Three-dimensional grid drawings of graphs, These Proceedings, 1997.Google Scholar
  11. 11.
    PINTER, R.Y.: On routing two-point nets across a channel. 19th ACNI-IEEE Design Automation Conf., 894–902, 1982.Google Scholar
  12. 12.
    ROSENBERG, A.L.: Three-Dimensional VLSI: A Case Study. Journal of the ACM, 30(3), 1983, pp 397–416.CrossRefGoogle Scholar
  13. 13.
    THOMPSON, C.D.: A complexity theory for VLSI. Ph.D. thesis, Carnegie-Mellon Univ. Pittsburgh, 1980.Google Scholar
  14. 14.
    WISE, D.S.: Compact layouts of banyan/FFT networks. VLSI Systems and Computations (H.T. Kung, B. Sproull, G. Steele, eds.) Computer Science Press, Rockville, Md., 1981, pp 186–195.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Tiziana Calamoneri
    • 1
  • Annalisa Massini
    • 2
  1. 1.Dipartimento di Matematica and Dipartimento ch Scienze dell'InformazioneUniversità di Roma “La Sapienza”Italy
  2. 2.Dipartimento di Scienze dell'InformazioneUniversità di Roma “La Sapienza”Italy

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