Packing random intervals |
| |
Authors: | E G Coffman Jr Bjorn Poonen Peter Winkler |
| |
Institution: | (1) AT&T Bell Laboratories, 07974 Murray Hill, NJ, USA;(2) Mathematical Sciences Research Institute, 94720 Berkeley, CA, USA |
| |
Abstract: | Summary Letn random intervalsI
1, ...,I
n be chosen by selecting endpoints independently from the uniform distribution on 0.1]. Apacking is a pairwise disjoint subset of the intervals; itswasted space is the Lebesgue measure of the points of 0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for largen, this best packing has wasted space
. It turns out that if the endpoints 0 and 1 are identified, so that the problem is now one of packing random arcs in a unit-circumference circle, then optimal wasted space is reduced toO(1/n). Interestingly, there is a striking difference between thesizes of the best packings: about logn intervals in the unit interval case, but usually only one or two arcs in the circle case. |
| |
Keywords: | 60D05 05B40 52A22 |
本文献已被 SpringerLink 等数据库收录! |
|