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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... (Update)
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.... In general, redundancies of a representation can be removed eciently using standard algorithms based on linear programming, see e.g. [13]. Now, we evaluate the complexity of Algorithm 4.1. Clearly, the major computational burden comes from solving LPs. Since the time...
...points. This amounts to solving n LPs. While the time complexity of this pure 12 LP method is polynomial and additional techniques [OSS95] can reduce the size of LPs, this might end up in a very time consuming job for large n (say 1; 000) There is a technique that might be...
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BibTeX entry: (Update)
T. Ottmann, S. Schuierer, and S. Soundaralakshmi. Enumerating extreme points in higher dimensions. In Proc. 12th Sympos. Theoretical Aspects of Comput. Sci., Lect. Notes in Comput. Sci., vol. 900, 562--570, 1995. http://citeseer.ist.psu.edu/ottmann95enumerating.html More
@inproceedings{ ottmann95enumerating,
author = "Thomas Ottmann and Sven Schuierer and S. Soundaralakshmi",
title = "Enumerating Extreme Points in Higher Dimensions",
booktitle = "Symposium on Theoretical Aspects of Computer Science",
pages = "562-570",
year = "1995",
url = "citeseer.ist.psu.edu/ottmann95enumerating.html" }
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