Average-case analysis of rectangle packings

E. G. Coffman, George S. Lueker, Joel Spencer, Peter M. Winkler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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(n1/2). Although tight bounds for the problem generalized to d > 2 dimensions remain an open problem, we have been able to show that ω(n1/2) and O((n logd-1 n)1/2) are asymptotic lower and upper bounds. In addition, we can prove that θ(nd/(d+1)) is a tight asymptotic bound for the case of random cubes.

Original languageEnglish (US)
Title of host publicationLATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings
Pages292-297
Number of pages6
Volume1776 LNCS
DOIs
StatePublished - 2000
Event4th Latin American Symposium on Theoretical Informatics, LATIN 2000 - Punta del Este, Uruguay
Duration: Apr 10 2000Apr 14 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1776 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th Latin American Symposium on Theoretical Informatics, LATIN 2000
CountryUruguay
CityPunta del Este
Period4/10/004/14/00

Fingerprint

Average-case Analysis
Set theory
Rectangle
Packing
Disjoint
Interval
Subset
Probability Model
Regular hexahedron
Upper and Lower Bounds
Cardinality
Open Problems

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Coffman, E. G., Lueker, G. S., Spencer, J., & Winkler, P. M. (2000). Average-case analysis of rectangle packings. In LATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings (Vol. 1776 LNCS, pp. 292-297). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1776 LNCS). https://doi.org/10.1007/10719839_30

Average-case analysis of rectangle packings. / Coffman, E. G.; Lueker, George S.; Spencer, Joel; Winkler, Peter M.

LATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings. Vol. 1776 LNCS 2000. p. 292-297 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1776 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Coffman, EG, Lueker, GS, Spencer, J & Winkler, PM 2000, Average-case analysis of rectangle packings. in LATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings. vol. 1776 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1776 LNCS, pp. 292-297, 4th Latin American Symposium on Theoretical Informatics, LATIN 2000, Punta del Este, Uruguay, 4/10/00. https://doi.org/10.1007/10719839_30
Coffman EG, Lueker GS, Spencer J, Winkler PM. Average-case analysis of rectangle packings. In LATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings. Vol. 1776 LNCS. 2000. p. 292-297. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/10719839_30
Coffman, E. G. ; Lueker, George S. ; Spencer, Joel ; Winkler, Peter M. / Average-case analysis of rectangle packings. LATIN 2000: Theoretical Informatics - 4th Latin American Symposium, Proceedings. Vol. 1776 LNCS 2000. pp. 292-297 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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