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:
-
i)
L is the minimal element of an order defined on the set of layouts of a graph with fixed boundary.
-
ii)
L may be constructed as the limit of the 1p-optimal layouts Lp of G.
-
iii)
If G is a planar graph with fixed boundary, then the optimal balanced layout L of G is ‘quasi-planar’.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
B.Becker, G.Hotz: ‘On the Optimal Layout of Planar Graphs with Fixed Boundary', T.R., 03/1983, SFB 124, Saarbrücken
H.G. Osthof: ‘Der minimale Kreis um eine endliche Punktmenge', Diplomarbeit, Saarbrücken 1983
M.I.Shamos, D.Hoey: ‘Closest-Point Problems', Proc. 16th IEEE Symp. on Foundations of Comput. Sci., Oct. 1975, pp. 151–162
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Becker, B., Osthof, H.G. (1984). Layouts with wires of balanced length. In: Mehlhorn, K. (eds) STACS 85. STACS 1985. Lecture Notes in Computer Science, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023991
Download citation
DOI: https://doi.org/10.1007/BFb0023991
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13912-6
Online ISBN: 978-3-540-39136-4
eBook Packages: Springer Book Archive