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Extending Partial Representations of Rectangular Duals with Given Contact Orientations

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Algorithms and Complexity (CIAC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12701))

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Abstract

A rectangular dual of a graph G is a contact representation of G by axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. The partial representation extension problem for rectangular duals asks whether a given partial rectangular dual can be extended to a rectangular dual, that is, whether there exists a rectangular dual where some vertices are represented by prescribed rectangles. Combinatorially, a rectangular dual can be described by a regular edge labeling (REL), which determines the orientations of the rectangle contacts. We characterize the RELs that admit an extension, which leads to a linear-time testing algorithm. In the affirmative, we can construct an extension in linear time.

Partially supported by DFG grants Ru 1903/3-1 and Wo 758/11-1.

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Authors and Affiliations

  1. Maastricht University, Maastricht, The Netherlands

    Steven Chaplick

  2. Universität Würzburg, Würzburg, Germany

    Philipp Kindermann, Jonathan Klawitter & Alexander Wolff

  3. Universität Passau, Passau, Germany

    Ignaz Rutter

Authors
  1. Steven Chaplick
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  2. Philipp Kindermann
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  3. Jonathan Klawitter
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  4. Ignaz Rutter
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  5. Alexander Wolff
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Editor information

Editors and Affiliations

  1. Sapienza University of Rome, Rome, Italy

    Tiziana Calamoneri

  2. Sapienza University of Rome, Rome, Italy

    Federico Corò

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Chaplick, S., Kindermann, P., Klawitter, J., Rutter, I., Wolff, A. (2021). Extending Partial Representations of Rectangular Duals with Given Contact Orientations. In: Calamoneri, T., Corò, F. (eds) Algorithms and Complexity. CIAC 2021. Lecture Notes in Computer Science(), vol 12701. Springer, Cham. https://doi.org/10.1007/978-3-030-75242-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-75242-2_24

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  • Online ISBN: 978-3-030-75242-2

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