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Algorithms for Packing Two Circles in a Convex Polygon

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Discrete and Computational Geometry (JCDCG 1998)

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

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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.

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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 

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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
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  2. Jurek Czyzowicz
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  3. Evangelos Kranakis
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  4. Anil Maheshwari
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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

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© 2000 Springer-Verlag Berlin Heidelberg

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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

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  • 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

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