Algorithmica

, Volume 9, Issue 1, pp 1–22 | Cite as

The slab dividing approach to solve the EuclideanP-Center problem

  • R. Z. Hwang
  • R. C. T. Lee
  • R. C. Chang
Article

Abstract

Givenn demand points on the plane, the EuclideanP-Center problem is to findP supply points, such that the longest distance between each demand point and its closest supply point is minimized. The time complexity of the most efficient algorithm, up to now, isO(n2p−1· logn). In this paper, we present an algorithm with time complexityO(n0(√P)).

Key words

Computational geometry NP-completeness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A. V., Hopcroft, J. E., and Ullman, J. D.,The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.Google Scholar
  2. Bentley, J. L., Multidimensional divide and conquer,Comm. ACM, Vol. 23, No. 4, 1980, pp. 214–229.Google Scholar
  3. Drezner, Z., On a modified one-center model,Management Sci., Vol. 27, 1981, pp. 848–851.Google Scholar
  4. Drezner, Z., The P-center problem.-Heuristics and optimal algorithms,J. Oper. Res. Soc., Vol. 35, No. 8, 1984, pp. 741–748.Google Scholar
  5. Drezner, Z., On the rectangular P-center problem,Naval Res. Logist. Quart., Vol. 34, 1987, pp. 229–234.Google Scholar
  6. Edelsbrunner, H.,Algorithms in Combinatorial Geometry, Springer-Verlag, New York, 1987.Google Scholar
  7. Helly, E., Über Mengen konvexer Körper mit gemeinschaftlichen Punkten,Jahresber. Deutsch. Math.-Verein., Vol. 32, 1923, pp. 175–176.Google Scholar
  8. Horowitz, E. and Sahni, S.,Fundamentals of Computer Algorithms, Computer Science Press, Rockville, MD, 1978.Google Scholar
  9. Lipton, R. and Tarjan, R. E., A separator theorem for planar graphs,SIAM J. Appl. Math., Vol. 36, No. 2, 1979, pp. 177–189.Google Scholar
  10. Lipton, R. and Tarjan, R. E., Applications of a planar separator theorem,SIAM J. Comput., Vol. 9, No. 3, 1980, pp. 615–627.Google Scholar
  11. Megiddo, N., Linear-Time algorithms for linear programming inR 3 and related problems,SIAM J. Comput., Vol. 12, No. 4, 1983, pp. 759–776.Google Scholar
  12. Megiddo, N. and Supowit, K. J., On the complexity of some common geometric location problems,SIAM J. Comput., Vol. 13, No. 1, 1984, pp. 1182–1196.Google Scholar
  13. Mehlhorn, K.,Data Structures and Algorithms 2: Graph Algorithms and NP-Completeness, Springer-Verlag, Berlin, 1984.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • R. Z. Hwang
    • 1
  • R. C. T. Lee
    • 1
    • 2
  • R. C. Chang
    • 2
    • 3
  1. 1.Institute of Computer ScienceNational Tsing Hua UniversityHsinchuTaiwan, Republic of China
  2. 2.Academia SinicaTaipeiTaiwan, Republic of China
  3. 3.Institute of Computer ScienceNational Chiao Tung UniversityHsinchuTaiwan, Republic of China

Personalised recommendations