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International Symposium on Graph Drawing and Network Visualization

GD 2020: Graph Drawing and Network Visualization pp 160–172Cite as

Schematic Representation of Biconnected Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12590))

Abstract

Suppose that a biconnected graph is given, consisting of a large component plus several other smaller components, each separated from the main component by a separation pair. We investigate the existence and the computation time of schematic representations of the structure of such a graph where the main component is drawn as a disk, the vertices that take part in separation pairs are points on the boundary of the disk, and the small components are placed outside the disk and are represented as non-intersecting lunes connecting their separation pairs. We consider several drawing conventions for such schematic representations, according to different ways to account for the size of the small components. We map the problem of testing for the existence of such representations to the one of testing for the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time and pseudo-polynomial-time algorithms.

This research was supported in part by MIUR Project “AHeAD” under PRIN 20174LF3T8, by H2020-MSCA-RISE Proj. “CONNECT” n\(^\circ \) 734922, and by Roma Tre University Azione 4 Project “GeoView”.

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Acknowledgments

Thanks to an anonymous reviewer for observing that computing a max-constrained book-embedding has a time complexity that is lower-bounded by the one of sorting.

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Authors and Affiliations

  1. Roma Tre University, Rome, Italy

    Giuseppe Di Battista, Fabrizio Frati, Maurizio Patrignani & Marco Tais

Authors
  1. Giuseppe Di Battista
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  2. Fabrizio Frati
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  3. Maurizio Patrignani
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  4. Marco Tais
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Corresponding author

Correspondence to Fabrizio Frati .

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Editors and Affiliations

  1. LaBRI, University of Bordeaux, Talence, France

    David Auber

  2. Charles University, Prague, Czech Republic

    Pavel Valtr

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Di Battista, G., Frati, F., Patrignani, M., Tais, M. (2020). Schematic Representation of Biconnected Graphs. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-68766-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68765-6

  • Online ISBN: 978-3-030-68766-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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