Discrete & Computational Geometry

, Volume 4, Issue 6, pp 605–610 | Cite as

On the ball spanned by balls

  • Nimrod Megiddo
Article

Abstract

The procedure for linear programming in linear time in fixed dimension is extended to solve in linear time certain nonlinear problems. Examples are the problem of finding the smallest ball enclosingn given balls, and the weighted-center problem in fixed dimension.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ch]
    R. Chandrasekaran, The weighted Euclidean 1-center problem,Operations Research Letters 1 (1982), 111–112.MATHMathSciNetCrossRefGoogle Scholar
  2. [Cl]
    K. Clarkson, Linear programming in\(O(n \times 3^{d^2 } )\) time,Information Processing Letters 22 (1986), 21–24.MathSciNetCrossRefGoogle Scholar
  3. [Co]
    R. Cole, Slowing down sorting networks to obtain faster sorting algorithms, in:Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science (1984), IEEE Computer Society Press, Los Angeles, 1984, pp. 255–260.Google Scholar
  4. [D1]
    M. E. Dyer, Linear-time algorithms for two- and three-variable linear programs,SIAM Journal on Computing 13 (1984), 31–45.MATHMathSciNetCrossRefGoogle Scholar
  5. [D2]
    M. E. Dyer, On a multidimensional search technique and its application tothe Euclidean one-center problem,SIAM Journal on Computing 15 (1986), 725–738.MATHMathSciNetCrossRefGoogle Scholar
  6. [M1]
    N. Megiddo, Linear-time algorithms for linear programming inR 3 and related problems, SIAMJournal on Computing 12 (1983), 759–776.MATHMathSciNetCrossRefGoogle Scholar
  7. [M2]
    N. Megiddo, The weighted Euclidean 1-center problem,Mathematics of Operations Research 8 (1983), 498–504.MATHMathSciNetCrossRefGoogle Scholar
  8. [M3]
    N. Megiddo, Linear programming in linear time when the dimension is fixed,Journal of the Association for Computing Machinery 31 (1984), 114–127.MATHMathSciNetCrossRefGoogle Scholar
  9. [MZ]
    N. Megiddo and E. Zemel, A randomizingO(n logn) algorithm for the weighted Euclidean 1-center problem,Journal of Algorithms 7 (1986), 358–368.MATHMathSciNetCrossRefGoogle Scholar
  10. [OKM]
    J. O'Rourke, S. R. Kosaraju, and N. Megiddo, Computing circular separability,Discrete & Computational Geometry 1 (1986), 105–113.MATHMathSciNetCrossRefGoogle Scholar
  11. [PS]
    R. Pollack and M. Sharir, Computing the geodesic center of a simple polygon, Technical Report No. 231, Courant Institute of Mathematical Sciences, New York University, July 1986.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • Nimrod Megiddo
    • 1
    • 2
  1. 1.IBM Almaden Research CenterSan JoseUSA
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

Personalised recommendations