Order of decay of the wasted space for a stochastic packing problem
成果类型：
Article
署名作者：
Rhee, WT
署名单位：
University System of Ohio; Ohio State University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2000
页码：
539-548
关键词：
摘要：
A packing of a collection of rectangles contained in [0, 1](2) is a disjoint subcollection; the wasted space is the measure of the area of the part of [0, 1]2 not covered by the subcollection. A simple packing has the further restriction that each vertical line meets at most one rectangle of the packing. Given a collection of N independent uniformly distributed subrectangles of [0, 1], we proved in a previous work that there exists a number K such that the wasted space W-N in an optimal simple packing of these rectangles satisfies for all N E-WN less than or equal to K/rootN exp K root log N. We prove here that 1/K rootN exp 1/K root log N less than or equal to EWN.