Skip to main content
SpringerLink
Log in

On the Rectangular Subset Closure of Point Sets

  • Conference paper
Computational Science and Its Applications – ICCSA 2005 (ICCSA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3480))

Included in the following conference series:

Abstract

Many applications like picture processing, data compression or pattern recognition require a covering of a set of points most often located in the (discrete) plane by rectangles due to some cost constraints. In this paper we introduce and study the concept of the rectangular subset closure of a point set M in the (discrete) plane which is aimed to provide some insight into the rectangular combinatorial structure underlying such a covering problem. We show that the rectangular subset closure of a set M is of size O(|M|2) and that it can be computed in time O(|M|2). The concepts and results are also generalized to the d-dimensional case.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boros, E., Hammer, P.L.: On Clustering Problems with Connected Optima in Euclidean Spaces. Discrete Mathematics 75, 81–88 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Calheiros, F.C., Lucena, A., de Souza, C.C.: Optimal Rectangular Partitions. Networks 41, 51–67 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hershberger, J., Suri, S.: Finding Tailored Partitions. Journal of Algorithms 12, 431–463 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hochbaum, D.S. (ed.): Approximation Algorithms for NP-hard problems. PWS Publishing, Boston (1996)

    Google Scholar 

  5. Porschen, S.: On Covering ℤ-Grid Points by Rectangles. In: ENDM, vol. 8 (2001)

    Google Scholar 

  6. Tanimoto, S.L., Fowler, R.J.: Covering Image Subsets with Patches. In: Proceedings of the fifty-first International Conference on Pattern Recognition, pp. 835–839 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, D-50969, Köln, Germany

    Stefan Porschen

Authors
  1. Stefan Porschen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W, T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, P.O. Box, I-06123, Perugia, Italy

    Antonio Laganà

  5. Institute of High Performance Computing, IHCP, 1 Science Park Road, 01-01 The Capricorn, Singapore Science Park II, 117528, Singapore

    Heow Pueh Lee

  6. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  7. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  8. OptimaNumerics Ltd, P.O. Box, Belfast, United Kingdom

    Chih Jeng Kenneth Tan

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Porschen, S. (2005). On the Rectangular Subset Closure of Point Sets. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424758_82

Download citation

  • DOI: https://doi.org/10.1007/11424758_82

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25860-5

  • Online ISBN: 978-3-540-32043-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation