Enumerating Extreme Points in Higher Dimensions

We consider the problem of enumerating all extreme points of a given set P of n points in d dimensions. We present a simple and practical algorithm which uses O(n) space and O(nm) time, where m is the number of extreme points of P. Our algorithm is designed to work even for highly degenerate input.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 time complexity O(n2) which significantly improves the O(n3) complexity of the naive algorithm.

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