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Abstract: Weintroduce a new method for finding several types of optimal k-point sets, minimizing perimeter, diameter, circumradius, and related measures, by testing sets of the O(k) nearest neighbors to each point. We argue that this is better in a number of ways than previous algorithms, whichwere based on high order Voronoi diagrams. Our technique allows us for the first time to efficiently maintain minimal sets as new points are inserted, to generalize our algorithms to higher dimensions, to... (Update)
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...that contains k of the n input points. The best known deterministic algorithm runs in time O(n log n nk log k) using O(n k log k) space [116, 84] (see also [111] and the best known randomized algorithm runs in O(n log n nk) expected time using O(nk) space, or in O(n log n nk...
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BibTeX entry: (Update)
J. Erickson and D. Eppstein, Iterated nearest neighbors and finding minimal polytopes. Discrete and Computational Geometry, (11) 1994, pp. 321--350. http://citeseer.ist.psu.edu/erickson94iterated.html More
@inproceedings{ eppstein93iterated,
author = "Eppstein and Erickson",
title = "Iterated Nearest Neighbors and Finding Minimal Polytopes",
booktitle = "{SODA}: {ACM}-{SIAM} Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)",
year = "1993",
url = "citeseer.ist.psu.edu/erickson94iterated.html" }
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