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May 1996 Packing random intervals
WanSoo T. Rhee, Michel Talagrand
Ann. Appl. Probab. 6(2): 572-576 (May 1996). DOI: 10.1214/aoap/1034968145


A packing of a collection of subintervals of [0, 1] is a pairwise disjoint subcollection of the intervals; its wasted space is the measure of the set of points not covered by the packing.

Consider n random intervals, $I_1, \dots, I_n$, chosen by selecting endpoints independently from the uniform distribution. We strengthen and simplify the results of Coffman, Poonen and Winkler, and we show that, for some universal constant K and for each $t \geq 1$, with probability greater than or equal to $1 - 1/n_t$, there is a packing with wasted space less than or equal to $Kt (\log n)^2 /n$.


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WanSoo T. Rhee. Michel Talagrand. "Packing random intervals." Ann. Appl. Probab. 6 (2) 572 - 576, May 1996.


Published: May 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0855.60048
MathSciNet: MR1398059
Digital Object Identifier: 10.1214/aoap/1034968145

Primary: 60G55 , 90B05

Keywords: asymptotic estimate , Packing , random intervals , wasted space

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 2 • May 1996
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