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

  • Kevin Balas
  • Csaba D. Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9198)

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.

Keywords

Grid Point Grid Line Product Order Planar Point Bend Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.California State University NorthridgeLos AngelesUSA
  2. 2.Los Angeles Mission CollegeSylmarUSA
  3. 3.Tufts UniversityMedfordUSA

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