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