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)


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.


Grid Point Grid Line Product Order Planar Point Bend Point 
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© 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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