Skip to main content
SpringerLink
Log in

Parametric search: three new applications

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

Parametric search is a useful tool in geometric optimization. Invented by Nimrod Megiddo in 1983, it has been widely used in computational geometry. Unfortunately, this technique has rarely been used in the combinatorial optimization community in China. In this paper, we introduce parametric search via three new geometric optimization applications.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agarwal P, Bereg S, Daescu O, Kaplan H, Ntafos S, Sharir M, Zhu B. Guarding a terrain by two watchtowers. Algorithmica (to appear)

  2. Agarwal P, Bereg S, Daescu O, Kaplan H, Ntafos S, Zhu B. Guarding a terrain by two watchtowers. In: Proc 21st Annu Sympos Comput Geom. 2005, 346–355

  3. Agarwal P, Sharir M, Toledo S. Applications of parametric searching in geometric optimization. In: Proceedings of the 3rd Annual ACM-SIAM Sympos on Discrete Algo (SODA’92). 1992, 72–82

  4. Agarwal P, Sharir M, Welzl E. The discrete 2-center problem. Discrete Comput Geom, 1998, 20: 287–305

    Article  MATH  MathSciNet  Google Scholar 

  5. Atallah M J, Chen D Z, Wagner H. An optimal parallel algorithm for the visibility of a simple polygon from a point. J ACM, 1991, 38(3): 516–533

    Article  MATH  Google Scholar 

  6. Ben-Moshe B, Katz M J, Mitchell J S B. A constant-factor approximation algorithm for optimal terrain guarding. In: Proc 16th Annu ACM-SIAM Sympos Discrete Algo. 2005, 515–524

  7. Bespamyatnikh S, Chen Z, Wang K, Zhu B. On the planar two-watchtower problem. In: Proc 7th Annu Internat Conf Computing and Combinatorics. 2001, 121–130

  8. Chan T. More planar two-center algorithms. Comput Geom Theory Appls, 1999, 13: 189–198

    MATH  Google Scholar 

  9. Clarkson K, Varadarajan K. Improved approximation algorithms for geometric set cover. In: Proc 21st Annu Sympos Comput Geom. 2005, 135–141

  10. Cole R. Slowing down sorting networks to obtain faster sorting algorithms. J ACM, 1987, 34: 200–208

    Article  MathSciNet  Google Scholar 

  11. Cole R, Sharir M. Visibility problems for polyhedral terrains. J Symbolic Comput, 1989, 7: 11–30

    Article  MathSciNet  Google Scholar 

  12. ElGindy H, Avis D. A linear time algorithm for computing the visibility polygon from a point. J Algorithms, 1981, 2(4): 186–197

    Article  MathSciNet  Google Scholar 

  13. Eppstein D. Faster construction of planar two-centers. In: Proc 8th Annu ACM-SIAM Sympos Discrete Algo. 1997, 131–138

  14. Guibas L, Hershberger J, Leven D, Sharir M, Tarjan R. Linear time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica, 1987, 2(2): 209–234

    Article  MATH  MathSciNet  Google Scholar 

  15. Halperin D, Sharir M, Goldberg A. The 2-center problem with obstacles. In: Proc 16th Annu Sympos Comput Geom, 2000, 80–90

  16. Joe B. On the correction of a linear time visibility polygon algorithm. Intl J Comput Math, 1990, 32: 155–172

    Article  MATH  Google Scholar 

  17. Joe B, Simpson R B. Correction to Lee’s visibility polygon algorithm. BIT, 1987, 27: 458–473

    Article  MATH  Google Scholar 

  18. Ko M T, Lee R C T, Chang J S. An optimal approximation algorithm for the rectilinear m-center problem. Algorithmica, 1990, 5: 341–352

    Article  MATH  MathSciNet  Google Scholar 

  19. Lee D T. Visibility of a simple polygon. Comput Vision Graph Image Process, 1983, 22: 207–221

    Article  MATH  Google Scholar 

  20. Megiddo N. Applying parallel computation algorithms in the design of serial algorithms. J ACM, 1983, 30: 852–865

    Article  MATH  MathSciNet  Google Scholar 

  21. Nilsson B. Guarding Art Galleries: Methods for Mobile Guards. Doctoral Thesis. Dept Comput Sci, Lund University, 1994

  22. van Oostrum R, Veltkamp R. Parametric search made practical. In: Proc 18th Annu Sympos Comput Geom. 2002, 1–9

  23. O’Rourke J. Art Gallery Theorems and Algorithms. Oxford: Oxford University Press, 1987

    MATH  Google Scholar 

  24. Preparata F P, Shamos M I. Computational Geometry: An Introduction. Berlin: Springer-Verlag, 1985

    Google Scholar 

  25. Sharir M. A near-linear algorithm for the planar 2-center problem. Discrete Comput Geom, 1997, 4: 125–134

    Article  MathSciNet  Google Scholar 

  26. Sharir M, Agarwal P K. Davenport Schinzel Sequences and Their Geometric Applications. New York: Cambridge University Press, 1995

    MATH  Google Scholar 

  27. Shin C -S, Kim J -H, Kim S -K, Chwa K -Y. Two-center problems for a convex polygon. In: Proc 6th European Sympos Algorithms (ESA’98). 1998, 199–210

  28. Zhu B. Computing the shortest watchtower of a polyhedral terrain in O(n log n) time. Comput Geom Theory Appls, 1997, 8: 181–193

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, Nishikyo, Kyoto, 615-8540, Japan

    Naoki Katoh

  2. Institute of Software, Chinese Academy of Sciences, Beijing, 100080, China

    Wencheng Wang

  3. State Key Lab for Manufacturing Systems Engineering, School of Management, Xi’an Jiaotong University, Xi’an, 710049, China

    Yinfeng Xu

  4. Department of Computer Science, Montana State University, Bozeman, MT, 59717-3880, USA

    Binhai Zhu

Authors
  1. Naoki Katoh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wencheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yinfeng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Binhai Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Binhai Zhu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Katoh, N., Wang, W., Xu, Y. et al. Parametric search: three new applications. Front. Math. China 5, 65–73 (2010). https://doi.org/10.1007/s11464-009-0049-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-009-0049-x

Keywords

Search

Navigation