Skip to main content
SpringerLink
Log in

Kinetic Red-Blue Minimum Separating Circle

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6831))

Abstract

In this paper, we study a kinetic version of the red-blue minimum separating circle problem, in which some points move with constant speed along straight line trajectories. We want to find the locus of the minimum separating circle over a period of time. We first consider two degenerate cases of this problem. In the first one (P1), we study the minimum separating circle problem with only one mobile blue point, and in the second one (P2), we study the minimum separating circle problem with only one mobile red point. Then, we give a solution for the general case (P3), in which multiple points are mobile.

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. Albers, G., Guibas, L.J., Mitchell, J.S.B., Roos, T.: Voronoi diagrams of moving points. Int. J. Comput. Geometry Appl. 8(3), 365–380 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aronov, B., Rappaport, D., Seara, C., Garijo, D., Núñez, Y., Urrutia, J.: Measuring the error of linear separators on linearly inseparable data. In: XIII Encuentros de Geometria Computacional, Zaragoza, España (2009)

    Google Scholar 

  3. Atallah, M.J.: Dynamic computational geometry (preliminary version). In: FOCS, pp. 92–99 (1983)

    Google Scholar 

  4. Basch, J., Guibas, L.J., Hershberger, J.: Data structures for mobile data. J. Algorithms 31(1), 1–28 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Basch, J., Guibas, L.J., Silverstein, C., Zhang, L.: A practical evaluation of kinetic data structures. In: Symposium on Computational Geometry, pp. 388–390 (1997)

    Google Scholar 

  6. Bitner, S., Cheung, Y.K., Daescu, O.: Minimum separating circle for bichromatic points in the plane. In: ISVD, pp. 50–55 (2010)

    Google Scholar 

  7. Demain, E., Einsenstat, S., Guibas, L., Schulz, A.: Kinetic minimum spanning circle. In: Proceedings of the Fall Workshop on Computational Geometry, New York, USA (2010)

    Google Scholar 

  8. Mitchell, J.S.B., Seara, C., Arkin, E.M., Hurtado, F., Skiena, S.: Some lower bounds on geometric separability problems. Int. J. Comput. Geometry Appl. 16(1), 1–26 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Seara, C., Hurtado, F., Sethia, S.: Red-blue separability problems in 3d. International Journal of Computational Geometry 15(2), 167–192 (2005)

    MathSciNet  MATH  Google Scholar 

  10. Fekete, S.: On the complexity of min-link red-blue separation (1992) (manuscript)

    Google Scholar 

  11. Fisk, S.: Separating point sets by circles, and the recognition of digital disks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 554–556 (July 1986)

    Google Scholar 

  12. Guibas, L.J.: Kinetic data structures: a state of the art report. In: WAFR 1998 (1998)

    Google Scholar 

  13. Hurtado, F., Mora, M., Ramos, P.A., Seara, C.: Separability by two lines and by nearly straight polygonal chains. Discrete Applied Mathematics 144(1-2), 110–122 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hurtado, F., Noy, M., Ramos, P.A., Seara, C.: Separating objects in the plane by wedges and strips. Discrete Applied Mathematics 109(1-2), 109–138 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Megiddo, N.: Linear-time algorithms for linear programming in R 3 and related problems. SIAM Journal on Computing 12(4), 759–776 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  16. O’Rourke, J., Kosaraju, S., Megiddo, N.: Computing circular separability. Discrete Computational Geometry 1, 105–113 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  17. Rahmati, Z., Zarei, A.: Combinatorial changes of euclidean minimum spanning tree of moving points in the plane. In: CCCG, pp. 43–45 (2010)

    Google Scholar 

  18. Roos, T.: Voronoi diagrams over dynamic scenes. Discrete Applied Mathematics 43(3), 243–259 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  19. Skyum, S.: A simple algorithm for computing the smallest enclosing circle. Information Processing Letters 37(3) (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Yam Ki Cheung, Ovidiu Daescu & Marko Zivanic

Authors
  1. Yam Ki Cheung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ovidiu Daescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marko Zivanic
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Zhejiang Normal University, 688 Yingbin Road, 321004, Jinhua, Zhejiang Province, China

    Weifan Wang  & Xuding Zhu  & 

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheung, Y.K., Daescu, O., Zivanic, M. (2011). Kinetic Red-Blue Minimum Separating Circle. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22616-8_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22615-1

  • Online ISBN: 978-3-642-22616-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation