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On the crossing-free, rectangular embedding of weighted graphs in the plane

  • Bernd Becker
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 145)

Abstract

In [1] M.J.Fischer and M.S.Paterson pointed out that finding the optimal planar layout of a weighted graph with respect to the L2-metric is NP-hard. We consider this problem with respect to the L1-city-block metric in the discrete and continuous case and show that it remains NP-hard.

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References

  1. [1]
    M.J.Fischer, M.S.Paterson: Optimal Tree Layout (Preliminary Version); Proc. Twelfth Annual ACM Symposium on Theory of Computing, pp. 177–189, 1980Google Scholar
  2. [2]
    B. Becker: Über die kreuzungsfreie, rechtwinklige Einbettung von gewichteten Graphen in die Ebene; Dissertation, Saarbrücken 1982Google Scholar
  3. [3]
    M.Tompa: An Optimal Solution to a Wire-routing Problem; Proc. Twelfth Annual ACM Symposium on Theory of Computing, pp. 201–210, 1980Google Scholar
  4. [4]
    A.S.LaPaugh: A Polynomial Time Algorithm for Optimal Routing around a Rectangle; Proc. Twenty-first Annual IEEE Symposium on Foundations of Computer Science, pp. 282–293, 1980Google Scholar
  5. [5]
    D.Dolev, K.Karplus, A.Siegel, A.Strong, J.D.Ullman: Optimal Wiring between Rectangles; Proc. Thirteenth Annual ACM Symposium on Theory of Computing, pp. 312–317, 1981Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Bernd Becker
    • 1
  1. 1.Fachbereich 10Universität des Saarlandes66 Saarbrücken

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