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Rectangle Visibility Graphs: Characterization, Construction, and Compaction

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

Non-overlapping axis-aligned rectangles in the plane define visibility graphs in which vertices are associated with rectangles and edges with visibility in either the horizontal or vertical direction. The recognition problem for such graphs is known to be NP-complete. This paper introduces the topological rectangle visibility graph.We give a polynomial time algorithm for recognizing such a graph and for constructing, when possible, a realizing set of rectangles on the unit grid. The bounding box of these rectangles has optimum length in each dimension. The algorithm provides a compaction tool: given a set of rectangles, one computes its associated graph, and runs the algorithm to get a compact set of rectangles with the same visibility properties.

Partially supported by NSF RUI grant CCR-0105507.

Partially supported by NSERC and FCAR.

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Author information

Authors and Affiliations

  1. Computer Science Department, Smith College, 01063, Northampton, MA, USA

    Ileana Streinu

  2. School of Comp. Sci., McGill Univ., H3A 2A7, Montreal, Quebec, Canada

    Sue Whitesides

Authors
  1. Ileana Streinu
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  2. Sue Whitesides
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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Streinu, I., Whitesides, S. (2003). Rectangle Visibility Graphs: Characterization, Construction, and Compaction. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_4

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  • DOI: https://doi.org/10.1007/3-540-36494-3_4

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  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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