Abstract
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(n 2) which significantly improves the O(n 3) 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).
This research is supported by the DFG-Project “Diskrete Probleme”, No. Ot 64/8-1.
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Ottmann, T., Schuierer, S., Soundaralakshmi, S. (1995). Enumerating extreme points in higher dimensions. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_105
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DOI: https://doi.org/10.1007/3-540-59042-0_105
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