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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2012: Graph-Theoretic Concepts in Computer Science pp 91–102Cite as

h-Quasi Planar Drawings of Bounded Treewidth Graphs in Linear Area

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7551))

Abstract

We study the problem of computing h-quasi planar drawings in linear area; in an h-quasi planar drawing the number of mutually crossing edges is at most h − 1. We prove that every n-vertex partial k-tree admits a straight-line h-quasi planar drawing in O(n) area, where h depends on k but not on n. For specific sub-families of partial k-trees, we present ad-hoc algorithms that compute h-quasi planar drawings in linear area, such that h is significantly reduced with respect to the general result. Finally, we compare the notion of h-quasi planarity with the notion of h-planarity, where each edge is allowed to be crossed at most h times.

Research supported in part by the MIUR project AlgoDEEP prot. 2008TFBWL4.

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Author information

Authors and Affiliations

  1. Dip. di Ingegneria Elettronica e dell’Informazione, Università degli Studi di Perugia, Italy

    Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta & Fabrizio Montecchiani

Authors
  1. Emilio Di Giacomo
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  2. Walter Didimo
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  3. Giuseppe Liotta
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  4. Fabrizio Montecchiani
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Caesarea Rothschild Institute (CRI), 31905, Haifa, Israel

    Martin Charles Golumbic

  2. The Academic College of Tel Aviv, Unit of Statistics and Probability Studies, 64044, Yaffo, Israel

    Michal Stern

  3. Shenkar College and Caesarea Rothschild Institute (CRI), University of Haifa, 31905, Haifa, Israel

    Avivit Levy

  4. Caesarea Rothschild Institute (CRI), 31905, Haifa, Israel

    Gila Morgenstern

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© 2012 Springer-Verlag Berlin Heidelberg

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Di Giacomo, E., Didimo, W., Liotta, G., Montecchiani, F. (2012). h-Quasi Planar Drawings of Bounded Treewidth Graphs in Linear Area. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_12

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  • DOI: https://doi.org/10.1007/978-3-642-34611-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34610-1

  • Online ISBN: 978-3-642-34611-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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