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Computational Geometry and Low Dimensional Linear Programs

  • Henry Wolkowicz
  • Adi Ben-Israel
Conference paper
Part of the NATO ASI Series book series (volume 51)

Abstract

Many areas (robotics, pattern recognition, computer graphics etc. ) offer problems requiring efficient computation of elementary planar geometric objects, e.g. the convex hull of a set, the intersectionof a line and a convex polytcpe, the distance between two line segments. Computational geometry, applying computer science methodology to such geometrical problems (see e.g. [3], [4]), has provided important algorithms and complexity results, typically under specific assumptions on the data structure.

Keywords

Data Structure Convex Hull Mathematical Program Computer Graphic Computational Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1).
    M.E. Dyer, Linear time algorithms for two-and three-variable linear programs, Siam J. Computing 13 (1984), 31–45. 186MathSciNetMATHCrossRefGoogle Scholar
  2. 2).
    N. Megiddo, Linear programming in linear time when the dimension is fixed, J. Assoc. Comput. March. 31 (1984), 114–127.MathSciNetMATHCrossRefGoogle Scholar
  3. 3).
    K. Mehlhorn, Data Structures and Algorithms 3: Multidimensional Searching and Computational Geometry, Springer, Berlin, 1984.Google Scholar
  4. 4).
    F.P. Preparata and M.I. Shamos, Computational Geometry — An Introduction, Springer, New York, 1985.Google Scholar
  5. 5).
    A. Schrijver, Theory of Linear and Integer Programming, J. Wiley, New York, 1986.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Henry Wolkowicz
    • 1
  • Adi Ben-Israel
    • 2
  1. 1.Dept. of Combinatorics and OptimizationUniversity of WaterlooCanada
  2. 2.Department of Mathematical SciencesUniversity of DelawareUSA

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