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Combinatorica

, Volume 35, Issue 1, pp 39–61 | Cite as

Packing anchored rectangles

  • Adrian Dumitrescu
  • Csaba D. Tóth
Original paper

Abstract

Let S be a set of n points in the unit square [0,1]2, one of which is the origin. We construct n pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in S, and the rectangles jointly cover at least a positive constant area (about 0.09). This is a first step towards the solution of a longstanding conjecture that the rectangles in such a packing can jointly cover an area of at least 1/2.

Mathematics Subject Classication (2000)

05B40 28A75 49Q10 52C15 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of WisconsinMilwaukeeUSA
  2. 2.Department of MathematicsCalifornia State University NorthridgeLos AngeleUSA
  3. 3.Department of Computer ScienceTufts UniversityMedfordUSA

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