Enumerating extreme points in higher dimensions

  • Th. Ottmann
  • S. Schuierer
  • S. Soundaralakshmi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 900)


We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present an algorithm with O(n) space and O(nm) time where m is the number of extreme points of P.

We also present an algorithm to compute the depth of each point of the given set of n points in d-dimensions. This algorithm has complexity O(n2) which significantly improves the O(n3) complexity of the previously best known deterministic algorithm. It also improves the best known randomized algorithm which has a expected running time of \(O(n^{3 - \frac{2}{{1 + [d/2]}} + \delta } )\) (for any fixed δ>0).


Computational Geometry 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Th. Ottmann
    • 1
  • S. Schuierer
    • 1
  • S. Soundaralakshmi
    • 1
  1. 1.Institut für InformatikUniversität FreiburgFreiburgFRG

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