A tight lower bound on the size of planar permutation networks

  • Maria Klawe
  • Tom Leighton
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 450)


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3. References

  1. [A87]
    N. Alon, Splitting necklaces, Advances in Math. 63(1987) pp.247–253.Google Scholar
  2. [AM85]
    N. Alon and V. Milman, λ1, isoperimetric inequalities for graphs, and superconcentrators, J. Comb. Theory B 38(1985), pp. 73–88.CrossRefGoogle Scholar
  3. [AKS90]
    A. Aggarwal, M. Klawe and P.Shor, Multi-layer grid embeddings for VLSI, to appear in Algorithmica.Google Scholar
  4. [AKLLW85]
    A. Aggarwal, M. Klawe, D. Lichtenstein, N. Linial, and A. Wigderson, Multilayer grid embeddings, Proc. IEEE 26th Ann. Symp. Found. Comp. Sci., 1985, pp. 186–196.Google Scholar
  5. [AKLLW90]
    A. Aggarwal, M. Klawe, D. Lichtenstein, N. Linial, and A. Wigderson, A lower bound on the area of permutation layouts, to appear in Algorithmica.Google Scholar
  6. [AW86]
    N. Alon and D. West, The Borsuk-Ulam theorem and bisection of necklaces, Proc. Amer. Math. Soc., 98(1986) pp. 623–628.Google Scholar
  7. [BL84]
    S. Bhatt and F. T. Leighton, A Framework for Solving VLSI Graph Layout Problems, JCSS Vol 28 No.2 April 1984, pp. 300–343.Google Scholar
  8. [BP77]
    N. K. Bose and K. A. Prabhu, Thickness of Graphs with Degree Constrained Vertices, IEEE Trans. on Circuits and Systems, Vol. CAS-24, No. 4, April 1977, pp. 184–190.CrossRefGoogle Scholar
  9. [CS78]
    M. Cutler and Y. Shiloach, Permutation Layout, Networks, Vol. 8, 1978, pp. 253–278.Google Scholar
  10. [GW85]
    C.H. Goldberg and D.B. West, Bisection of circle colorings, SIAM J. Alg. Disc. Math., 6(1985) pp. 93–106.Google Scholar
  11. [KKF79]
    E. S. Kuh, T. Kashiwabara, and T. Fujisawa, On Optimum Single Row-Routing, IEEE Trans. on Circuits and Systems, Vol. CAS-26, No. 6, June 1979, pp. 361–368.CrossRefGoogle Scholar
  12. [Ka80]
    Y. Kajitani, On Via Hole Minimization of Routings on a Two-Layer Board, Tech. Report, Dept. of Elec. Engineering, Tokyo Institute of Technology, Japan, 1980.Google Scholar
  13. [L81]
    F. T. Leighton, Layouts for the Shuffle-Exchange Graph and Lower Bound Techniques for VLSI, Ph. D. thesis, Dept. of Math., MIT, 1981.Google Scholar
  14. [L82]
    F. T. Leighton, A layout strategy for VLSI which is provably good, Proc. ACM Ann. Symp. Theory of Comp., 1982, pp. 85–98.Google Scholar
  15. [L84]
    F. T. Leighton, New Lower Bound Techniques for VLSI, Math Systems Theory 17(1984), pp. 47–70.CrossRefGoogle Scholar
  16. [LLS89]
    F.T.Leighton, C.E.Leiserson and E.Schwabe, Theory of parallel and VLSI computation, MIT/LCS/RRS 6 Research Seminar Series, Lecture Notes for 18.435/6.848, March 89.Google Scholar
  17. [LT79]
    R. J. Lipton and R. E. Tarjan, A Separator Theorem for Planar Graphs, SIAM J. Appl. Math., 36 (1979) 177–189.CrossRefGoogle Scholar
  18. [Ri82]
    R. Rivest, The Placement and Interconnect System, Proc. 19th Design Automation Conference, 1982, pp. 475–481.Google Scholar
  19. [Sh80]
    I. Shirakawa, Letter to the Editor: Some Comments on Permutation Layout, Networks, Vol. 10, 1980, pp. 179–182.Google Scholar
  20. [So74]
    H.C. So, Some Theoretical Results on the Routing of Multilayer Printed Wiring Boards, 1974 IEEE Int. Symp. on Circuits and Systems, pp. 296–303.Google Scholar
  21. [TKS76]
    B. S. Ting, E. S. Kuh, and I. Shirakawa, The Multilayer Routing Problem: Algorithms and Necessary and Sufficient Conditions for the SIngle-Row Single Layer Case, IEEE Trans. of Circuits and Systems, Vol. CAS-23, No. 12, 1979, pp. 768–778.CrossRefGoogle Scholar
  22. [TK82]
    S. Tsukiyama and E. S. Kuh, Double-Row Planar routing and Permutation Layout, Networks, Vol. 12, 1982, pp. 287–316.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Maria Klawe
    • 1
  • Tom Leighton
    • 2
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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