Advertisement

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)

Abstract

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’.

     

Keywords

Planar Graph Minimal Element Optimal Layout Graph Edge Planar Layout 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations