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Packing random rectangles
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  • Published: August 2001

Packing random rectangles

  • E.G. Coffman, Jr.1,
  • George S. Lueker2,
  • Joel Spencer3 &
  • …
  • Peter M. Winkler4 

Probability Theory and Related Fields volume 120, pages 585–599 (2001)Cite this article

  • 91 Accesses

  • 6 Citations

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Abstract.

A random rectangle is the product of two independent random intervals, each being the interval between two random points drawn independently and uniformly from [0,1]. We prove that te number C n of items in a maximum cardinality disjoint subset of n random rectangles satisfies

where K is an absolute constant. Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we are able to show that, for some absolute constat K,

Finally, for a certain distribution of random cubes we show that for some absolute constant K, the number Q n of items in a maximum cardinality disjoint subset of the cubes satisies

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Authors and Affiliations

  1. Electrical Engineering Department, Columbia University, New York, NY 10027, USA., , , , , , US

    E.G. Coffman, Jr.

  2. Information and Computer Science Department, University of California, Irvine, CA 92697-3425, USA. e-mail: lueker@ics.uci.edu, , , , , , US

    George S. Lueker

  3. Mathematics Department, New York University, New York, NY 10003, USA, , , , , , US

    Joel Spencer

  4. Bell Labs, Lucent Technologies, 700 Mountain Avenue, Murray Hill, NJ 07974, USA, , , , , , US

    Peter M. Winkler

Authors
  1. E.G. Coffman, Jr.
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  2. George S. Lueker
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  3. Joel Spencer
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  4. Peter M. Winkler
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Additional information

Received: 1 September 1999 / Revised version: 3 November 2000 / Published online: 14 June 2001

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Coffman, Jr., E., Lueker, G., Spencer, J. et al. Packing random rectangles. Probab Theory Relat Fields 120, 585–599 (2001). https://doi.org/10.1007/PL00008793

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  • Issue Date: August 2001

  • DOI: https://doi.org/10.1007/PL00008793

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  • Mathematics Subject Classification (2000): Primary 52C17; Secondary 05C69, 52C15, 60D05
  • Key words or phrases:n-dimensional packing – 2-dimensional packing – Intersection graphs – Independent sets – Probabilistic analysis of optimization problems
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