Weighted orthogonal linear L-approximation and applications

  • Michael E. Houle
  • Hiroshi Imai
  • Keiko Imai
  • Jean-Marc Robert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)


Let S={s1, s2,...,s n } be a set of sites in E d , where every site s i has a positive real weight ω i . This paper gives an algorithm to find a weighted orthogonal L-approximation hyperplane for S. The algorithm is shown to require O(nlogn) time and O(n) space for d=2, and O(n[d/2+1]) time and O(n[(d+1)/2]) space for d>2. The L-approximation algorithm will be adapted to solve the problem of finding the width of a set of n points in E d , and the problem of finding a stabbing hyperplane for a set of n hyperspheres in E d with varying radii. The time and space complexities of the width and stabbing algorithms are seen to be the same as those of the L-approximation algorithm.


Convex Hull Time Algorithm Feasibility Region Convex Polytope Supporting Hyperplane 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Michael E. Houle
    • 1
  • Hiroshi Imai
    • 2
  • Keiko Imai
    • 3
  • Jean-Marc Robert
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada
  2. 2.Department of Computer Science and Communication EngineeringKyushu UniversityFukuokaJapan
  3. 3.Information Science CenterKyushu Institute of Technology IizukaFukuokaJapan

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