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 (formula presented) (for any fixed δ > 0).
CITATION STYLE
Ottmann, T., Schuierer, S., & Soundaralakshmi, S. (1995). Enumerating extreme points in higher dimensions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 900, pp. 562–570). Springer Verlag. https://doi.org/10.1007/3-540-59042-0_105
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