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Orthogonal Compaction: Turn-Regularity, Complete Extensions, and Their Common Concept

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Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1182))

Abstract

The compaction problem in orthogonal graph drawing aims to construct efficient drawings on the orthogonal grid. The objective is to minimize the total edge length or area of a planar orthogonal grid drawing. However, any collisions, i.e. crossing edges, overlapping faces, or colliding vertices, must be avoided. The problem is NP-hard. Two common compaction methods are the turn-regularity approach by Bridgeman et al. [4] and the complete-extension approach by Klau and Mutzel [23]. Esser [14] has shown that both methods are equivalent and follow a common concept to avoid collisions.

We present both approaches and their common concept in detail. We introduce an algorithm to transform the turn-regularity formulation into the complete-extension formulation and vice versa in \(\mathcal {O}(n)\) time, where n is the number of vertices.

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Acknowledgements

I would like to thank Prof. Michael Jünger, University of Cologne, and his amazing team, which committed itself to Graph Drawing, enthused me with this area of research and always supported me with explanations, discussions, and suggestions: Christiane Spisla, Martin Gronemann, Sven Mallach, Francesco Mambelli, Daniel Schmidt.

My special thanks go to Joachim Köhler and all my colleagues at Fraunhofer IAIS, who support me advancing my research on Graph Drawing and bringing it together with projects from the area of document processing and table recognition.

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Authors and Affiliations

  1. Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS, Sankt Augustin, Germany

    Alexander M. Esser

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  1. Alexander M. Esser
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Correspondence to Alexander M. Esser .

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Editors and Affiliations

  1. University of Lisbon, Lisbon, Portugal

    Ana Paula Cláudio

  2. University of Rennes 1, Rennes, France

    Kadi Bouatouch

  3. University of Genoa, Genoa, Italy

    Manuela Chessa

  4. Mines ParisTech, Paris, France

    Alexis Paljic

  5. Linnaeus University, Växjö, Sweden

    Andreas Kerren

  6. French Civil Aviation University (ENAC), Toulouse, France

    Christophe Hurter

  7. University Jean Monnet, Saint-Etienne, France

    Alain Tremeau

  8. University of Catania, Catania, Italy

    Giovanni Maria Farinella

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Esser, A.M. (2020). Orthogonal Compaction: Turn-Regularity, Complete Extensions, and Their Common Concept. In: Cláudio, A., et al. Computer Vision, Imaging and Computer Graphics Theory and Applications. VISIGRAPP 2019. Communications in Computer and Information Science, vol 1182. Springer, Cham. https://doi.org/10.1007/978-3-030-41590-7_8

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  • DOI: https://doi.org/10.1007/978-3-030-41590-7_8

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