Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Expected wasted space of optimal simple rectangle packing
Download PDF
Download PDF
  • Published: 11 November 2004

Expected wasted space of optimal simple rectangle packing

  • Michel Talagrand1,2 

Probability Theory and Related Fields volume 131, pages 145–153 (2005)Cite this article

  • 80 Accesses

  • Metrics details

Abstract.

A simple packing of a collection of rectangles contained in [0,1]2 is a disjoint subcollection such that each vertical line meets at most one rectangle of the packing. The wasted space of the packing is the surface of the area of the part of [0,1]2 not covered by the packing. We prove that for a certain number L, for all N≥2, the wasted space W N in an optimal simple packing of N independent uniformly distributed rectangles satisfies

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Coffman Jr., E.G., Lueker, G.S.: Probabilistic Analysis of Packing and Partitioning Algorithms. John Wiley & Sons Ltd. New York, 1991

  2. Coffman Jr., E.G., Poonen, B., Winkler, P.: Packing random intervals. Prob. Th. Relat. Fields 102 (1), 105–121 (1995)

    MATH  Google Scholar 

  3. Rhee, W.: Some exact rates for the random weighted interval packing problem. Random Structures & Algorithms 15 (2), 165–175 (1999)

    Google Scholar 

  4. Rhee, W.: Order of decay of the wasted space for a stochastic packing problem. Annals of Applied Probability 10 (2), 539–548 (2000)

    Google Scholar 

  5. Rhee, W.: Packing rectangles and intervals. International Journal of Computer Mathematics 76, 479–488 (2001)

    MATH  Google Scholar 

  6. Rhee, W.: Packing random rectangles of given volume, Math. Oper. Res. 27 (1), 244–252 (2002)

    Article  Google Scholar 

  7. Rhee, W., Talagrand, M.: Packing random intervals. The Annals of Applied Probability. 6 (2), 572–576 (1996)

    MATH  Google Scholar 

  8. Rhee, W., Talagrand, M.: The random weighted interval packing problem: The intermediate density case. Mathematics of Operations Research 25 (1), 105–117 (2000)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Mathématiques, Université Paris VI, 4 Place Jussieu, 75230, Paris Cedex 05, France

    Michel Talagrand

  2. Departement of Mathematics, The Ohio-State University, Columbus, OH, 43210, USA

    Michel Talagrand

Authors
  1. Michel Talagrand
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work partially supported by an N.S.F. grant.

Mathematics Subject Classification (2000): 60D05

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Talagrand, M. Expected wasted space of optimal simple rectangle packing. Probab. Theory Relat. Fields 131, 145–153 (2005). https://doi.org/10.1007/s00440-003-0299-6

Download citation

  • Received: 24 May 2003

  • Revised: 06 September 2003

  • Published: 11 November 2004

  • Issue Date: February 2005

  • DOI: https://doi.org/10.1007/s00440-003-0299-6

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Key words or phrases:

  • Random rectangle packing
  • Interval packing
  • Optimal packing
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature