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Interdisciplinary Workshop on Informatics and Psychology

IPsy 1988: Visualization in Human-Computer Interaction pp 1–15Cite as

Nice drawings of graphs are computationally hard

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 439))

Abstract

How to draw a graph? And more importantly, how to draw it nicely? As a formal approach to this problem we propose graph embeddings. A graph embedding is a mapping from a guest graph into a host graph. Graph embeddings are very rich in their descriptive capabilities. These should suffice to capture all instances from real applications in an appropriate way. Graph embeddings offer various parameters for optimizations, which are used to describe aestetics in a formal and uniform way. Thus, we measure the niceness of a drawing by the values of its aestetic parameters, such as area, width, expansion, maximal and total edge length, or non-planarity. However, in this general framework and from an algorithmic point of view optimal embeddings or equivalently nice drawings of graphs are intractable. In general, they are NP-complete, which means that one must pay for nice drawings with a high computational effort. This fact holds even for trees. To the contrary, there are drawings of trees which satisfy the upper and lower bounds up to some constant factor and are computable in polynomial time.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik, Universität Passau, Innstr. 33, D 8390, Passau, F. R. Germany

    Franz J. Brandenburg

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  1. Franz J. Brandenburg
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Peter Gorny Michael J. Tauber

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© 1990 Springer-Verlag Berlin Heidelberg

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Brandenburg, F.J. (1990). Nice drawings of graphs are computationally hard. In: Gorny, P., Tauber, M.J. (eds) Visualization in Human-Computer Interaction. IPsy 1988. Lecture Notes in Computer Science, vol 439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52698-6_1

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  • DOI: https://doi.org/10.1007/3-540-52698-6_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52698-8

  • Online ISBN: 978-3-540-47102-8

  • eBook Packages: Springer Book Archive

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