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European Symposium on Algorithms

ESA 2014: Algorithms - ESA 2014 pp 87–99Cite as

Improved Approximation Algorithms for Box Contact Representations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

Abstract

We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called Contact Representation of Word Networks (Crown) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Crown is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, Max-Crown, in which realizing each desired adjacency yields a certain profit.

We show that the problem is APX-complete on bipartite graphs of bounded maximum degree. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we consider several planar graph classes (stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit.

The work of M. A. Bekos is implemented within the framework of the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State. Ph. Kindermann and A. Wolff acknowledge support by the ESF EuroGIGA project GraDR. S. Kobourov and S. Pupyrev are supported by NSF grants CCF-1115971 and DEB 1053573.

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany

    Michael A. Bekos

  2. Lehrstuhl für Informatik I, Universität Würzburg, Germany

    Thomas C. van Dijk, Martin Fink, Philipp Kindermann, Joachim Spoerhase & Alexander Wolff

  3. Department of Computer Science, University of Arizona, USA

    Stephen Kobourov & Sergey Pupyrev

  4. Institute of Mathematics and Computer Science, Ural Federal University, Russia

    Sergey Pupyrev

  5. Department of Computer Sicence, University of California, Santa Barbara, USA

    Martin Fink

Authors
  1. Michael A. Bekos
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  2. Thomas C. van Dijk
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  3. Martin Fink
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  4. Philipp Kindermann
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  5. Stephen Kobourov
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  6. Sergey Pupyrev
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  7. Joachim Spoerhase
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  8. Alexander Wolff
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Editor information

Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Andreas S. Schulz

  2. Karlsruhe Institute of Technology (KIT), Kaiserstruhe 12, 76131, Karlsruhe, Germany

    Dorothea Wagner

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Bekos, M.A. et al. (2014). Improved Approximation Algorithms for Box Contact Representations. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_8

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  • DOI: https://doi.org/10.1007/978-3-662-44777-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44776-5

  • Online ISBN: 978-3-662-44777-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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