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On the Number of Anchored Rectangle Packings for a Planar Point Set

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Computing and Combinatorics (COCOON 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9198))

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Abstract

We consider packing axis-aligned rectangles \(r_1,\ldots , r_n\) in the unit square \([0,1]^2\) such that a vertex of each rectangle \(r_i\) is a given point \(p_i\) (i.e., \(r_i\) is anchored at \(p_i\)); and explore the combinatorial structure of all locally maximal configurations. When the given points are lower-left corners of the rectangles, then the number of maximal packings is shown to be at most \(2^nC_n\), where \(C_n\) is the nth Catalan number. The number of maximal packings remains exponential in n when the points may be arbitrary corners of the rectangles. Our upper bounds are complemented with exponential lower bounds.

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Authors and Affiliations

  1. California State University Northridge, Los Angeles, CA, USA

    Kevin Balas & Csaba D. Tóth

  2. Los Angeles Mission College, Sylmar, CA, USA

    Kevin Balas

  3. Tufts University, Medford, MA, USA

    Csaba D. Tóth

Authors
  1. Kevin Balas
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  2. Csaba D. Tóth
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Corresponding author

Correspondence to Csaba D. Tóth .

Editor information

Editors and Affiliations

  1. Beijing University of Technology, Beijing, China

    Dachuan Xu

  2. University of New Brunswick, Fredericton, Canada

    Donglei Du

  3. University of Texas at Dallas, Richardson, USA

    Dingzhu Du

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Balas, K., Tóth, C.D. (2015). On the Number of Anchored Rectangle Packings for a Planar Point Set. In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_30

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  • DOI: https://doi.org/10.1007/978-3-319-21398-9_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21397-2

  • Online ISBN: 978-3-319-21398-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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