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
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 1 September 1999 / Revised version: 3 November 2000 / Published online: 14 June 2001
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/PL00008793