Layouts with wires of balanced length

  • B. Becker
  • H. G. Osthof
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 182)


For any graph (with fixed boundary) there exists a layout, which minimizes the maximum distance of any node to its neighbours. This layout balances the length of the wires (corresponding to graph edges) and is called (length-) balanced layout.

Furthermore the existence of a unique ‘optimal’ balanced layout L with the following properties is proved:
  1. i)

    L is the minimal element of an order defined on the set of layouts of a graph with fixed boundary.

  2. ii)

    L may be constructed as the limit of the 1p-optimal layouts Lp of G.

  3. iii)

    If G is a planar graph with fixed boundary, then the optimal balanced layout L of G is ‘quasi-planar’.



Planar Graph Minimal Element Optimal Layout Graph Edge Planar Layout 
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  1. [BeHo]
    B.Becker, G.Hotz: ‘On the Optimal Layout of Planar Graphs with Fixed Boundary', T.R., 03/1983, SFB 124, SaarbrückenGoogle Scholar
  2. [Os]
    H.G. Osthof: ‘Der minimale Kreis um eine endliche Punktmenge', Diplomarbeit, Saarbrücken 1983Google Scholar
  3. [ShHo]
    M.I.Shamos, D.Hoey: ‘Closest-Point Problems', Proc. 16th IEEE Symp. on Foundations of Comput. Sci., Oct. 1975, pp. 151–162Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • B. Becker
    • 1
  • H. G. Osthof
    • 1
  1. 1.Fachbereich 10Universität des SaarlandesSaarbrückenWest Germany

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