Average-case analysis of rectangle packings

Authors

E. G. Coffman, New Jersey Institute of Technology
George S. Lueker, University of California, Irvine
Joel Spencer, New York University
Peter M. Winkler, Nokia Bell Labs

Document Type

Conference Proceeding

Publication Date

12-1-2000

Abstract

We study the average-case behavior of algorithms for finding a maximal disjoint subset of a given set of rectangles. In the probability model, a random rectangle is the product of two independent random intervals, each being the interval between two points drawn uniformly at random from [0, 1]. We have proved that the expected cardinality of a maximal disjoint subset of n random rectangles has the tight asymptotic bound θ(n^1/2). Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we have been able to show that ω(n^1/2) and O((n log^d-1 n)^1/2) are asymptotic lower and upper bounds. In addition, we can prove that θ(n^d/(d+1)) is a tight asymptotic bound for the case of random cubes. © Springer-Verlag Berlin Heidelberg 2000.

Identifier

84896754274 (Scopus)

ISBN

[3540673067, 9783540673064]

Publication Title

Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics

External Full Text Location

https://doi.org/10.1007/10719839_30

e-ISSN

16113349

ISSN

03029743

First Page

292

Last Page

297

Volume

1776 LNCS

Recommended Citation

Coffman, E. G.; Lueker, George S.; Spencer, Joel; and Winkler, Peter M., "Average-case analysis of rectangle packings" (2000). Faculty Publications. 15516.
https://digitalcommons.njit.edu/fac_pubs/15516