Probability Theory and Related Fields

, Volume 120, Issue 4, pp 585-599

First online:

Packing random rectangles

  • E.G. Coffman, Jr.Affiliated withElectrical Engineering Department, Columbia University, New York, NY 10027, USA.
  • , George S. LuekerAffiliated withInformation and Computer Science Department, University of California, Irvine, CA 92697-3425, USA. e-mail:
  • , Joel SpencerAffiliated withMathematics Department, New York University, New York, NY 10003, USA
  • , Peter M. WinklerAffiliated withBell Labs, Lucent Technologies, 700 Mountain Avenue, Murray Hill, NJ 07974, USA

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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
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