Skip to main content
SpringerLink
Log in

Algorithms for Packing Two Circles in a Convex Polygon

  • Conference paper
Discrete and Computational Geometry (JCDCG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1763))

Included in the following conference series:

Abstract

We consider algorithms for packing two circles in a given n-vertex convex polygon. The first algorithm outputs a pair of equal non-overlapping circles of maximum radius and has running time O(n). The second algorithm outputs a pair of non-overlapping circles whose sum of radii is maximum and has running time O(n 2).

Research supported in part by NSERC (Natural Sciences and Engineering Research Council of Canada.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aggarwal, A., Guibas, L., Saxe, J., Shor, P.: A Linear Time Algorithm for Constructing the Voronoi Diagram of a Convex Polygon. Discrete and Computational Geometry 4(6), 591–604 (1989)

    MATH  MathSciNet  Google Scholar 

  2. Biedl, T., Demaine, E., Demaine, M., Lubiw, A., Toussaint, G.: Hiding disks in folded polygons. In: Proceedings of the 10th Can. Conf. on Comp. Geom. (1998)

    Google Scholar 

  3. Chin, F., Snoeyink, J., Wang, C.A.: Finding the Medial Axis of a Simple Polygon in Linear Time. In: Staples, J., Katoh, N., Eades, P., Moffat, A. (eds.) ISAAC 1995. LNCS, vol. 1004, pp. 382–391. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  4. Croft, H.T., Falconer, K.J., Guy, R.K.: Unsolved Problems in Geometry. Springer, Heidelberg (1991)

    MATH  Google Scholar 

  5. Lee, D.T.: Medial Axis Transformation of a Planar Shape. IEEE Tran. PAMI 4, 363–369 (1982)

    MATH  Google Scholar 

  6. O’Rourke, J.: Computational Geometry in C. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  7. Preparata, F.P., Shamos, M.I.: Computational Geometry: An Introduction. Springer, New York (1985)

    Google Scholar 

  8. Sharir, M.: A Near Linear Algorithm for the Planar 2-Center Problem. In: Proceedings of ACM Computational Geometry Conference, pp. 106–112 (1996)

    Google Scholar 

  9. Shin, C., Kim, J., Kim, S.K., Chwa, K.: Two-Center Problems for a Convex Polygon. In: Proceedings of ESA (1998) (to appear)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Prosenjit Bose, Evangelos Kranakis & Anil Maheshwari

  2. Dept. Informatique, Univ. du Québec à Hull, Hull, Québec, J8X 3X7, Canada

    Jurek Czyzowicz

Authors
  1. Prosenjit Bose
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jurek Czyzowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evangelos Kranakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anil Maheshwari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, 316-8511, Hitachi Ibaraki, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido, Shimizu, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bose, P., Czyzowicz, J., Kranakis, E., Maheshwari, A. (2000). Algorithms for Packing Two Circles in a Convex Polygon. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-46515-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67181-7

  • Online ISBN: 978-3-540-46515-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation