Packing anchored rectangles

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.

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Correspondence to Adrian Dumitrescu.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 23rd ACM-SIAM Symposium on Discrete Algorithms, (SODA 2012), Kyoto, Japan, January 2012.

Supported in part by the NSF grant DMS-1001667.

Supported in part by the NSERC grant RGPIN 35586 and the NSF grant CCF-0830734.

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Dumitrescu, A., Tóth, C.D. Packing anchored rectangles. Combinatorica 35, 39–61 (2015). https://doi.org/10.1007/s00493-015-3006-1

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Mathematics Subject Classication (2000)

  • 05B40
  • 28A75
  • 49Q10
  • 52C15