Skip to main content

Placing a Given Number of Base Stations to Cover a Convex Region

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3741))

Abstract

An important problem of mobile communication is placing a given number of base-stations in a given convex region, and to assign range to each of them such that every point in the region is covered by at least one base-station, and the maximum range assigned is minimized. The algorithm proposed in this paper uses Voronoi diagram, and it works for covering a convex region of arbitrary shape. Experimental results justify the efficiency of our algorithm and the quality of the solution produced.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. de Berg, M., Van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry Algorithms and Applications. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  2. Fowler, R.J., Paterson, M.S., Tanimoto, S.L.: Optimal packing and covering in the plane are NP-complete. Information Processing Letters 12, 133–137 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  3. Heppes, A., Melissen, J.B.M.: Covering a rectangle with equal circles. Periodica Mathematica Hungarica 34, 65–81 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hwang, R.Z., Lee, R.C.T., Chang, R.C.: The slab dividing approach to solve the Euclidean p-center problem. Algorithmica 9, 1–22 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Mehlhorn, K., Nher, S.: The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  6. Melissen, J.B.M., Schuur, P.C.: Covering a rectangle with six and seven circles. Discrete Applied Mathematics 99, 149–156 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Melissen, J.B.M., Schuur, P.C.: Improved covering a rectangle with six and seven circles. Electronic J. on Combinatorics 3–R32 (1996)

    Google Scholar 

  8. Nurmela, K.J.: Conjecturally optimal coverings of an equilateral triangle with up to 36 equal circles. Experimental Mathematics 9 (2000)

    Google Scholar 

  9. Nurmela, K.J., Ostergard, P.R.J.: Covering a square with up to 30 Equal Circles, Research Report HUT-TCS-A62, Laboratory for Theoretical Computer Science, Helsinky University of Technology (2000)

    Google Scholar 

  10. Megiddo, N.: Linear-time algorithms for linear programming in R 3 and related problems. SIAM Journal on Computing 12, 759–776 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  11. Tarnai, T., Gasper, Z.: Covering a square by equal circles. Elementary Mathematics 50, 167–170 (1995)

    MATH  Google Scholar 

  12. Verblunsky, S.: On the least number of unit circles which can cover a square. Journal of the London Mathematical Society 24, 164–170 (1949)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Das, G.K., Das, S., Nandy, S.C., Sinha, B.P. (2005). Placing a Given Number of Base Stations to Cover a Convex Region. In: Pal, A., Kshemkalyani, A.D., Kumar, R., Gupta, A. (eds) Distributed Computing – IWDC 2005. IWDC 2005. Lecture Notes in Computer Science, vol 3741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603771_6

Download citation

  • DOI: https://doi.org/10.1007/11603771_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30959-8

  • Online ISBN: 978-3-540-32428-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics