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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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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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118 Ray shooting and parametric search (context) - Agarwal, Matousek - 1992
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80 Slowing down sorting networks to obtain faster sorting algor.. (context) - Cole - 1987
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74 Topologically sweeping an arrangement (context) - Edelsbrunner, Guibas - 1989
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63 A combinatorial problem in geometry (context) - Erdos, Szekeres - 1935
60 The power of geometric duality (context) - Chazelle, Guibas et al. - 1985
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52 Quasi-optimal upper bounds for simplex range searching and n.. (context) - Chazelle, Sharir et al. - 1990
44 Static and dynamic algorithms for k-point clustering problem.. (context) - Datta, Lenhof et al. - 1993
43 Iterated nearest neighbors and finding minimal polytopes - Eppstein, Erickson - 1992
42 algorithm for the all-nearest-neighbors problem (context) - Vaidya, log - 1989
36 Finding tailored partitions (context) - Hershberger, Suri - 1989
27 points with minimum diameter and related problems (context) - Aggarwal, Imai et al. - 1991
24 New upper bounds in Klee's measure problem (context) - Overmars, Yap - 1991
22 Simple algorithm for enumerating interpoint distances and fi.. (context) - Dickerson, Drysdale et al. - 1993
21 Sets with no emptyconvex 7-gons (context) - Horton - 1983
21 An optimal convex hull algorithm and new results on cuttings (context) - Chazelle - 1991
16 Finding minimum area k-gons - Eppstein, Overmars et al. - 1992
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10 Finding smallest polygons (context) - Dobkin, Drysdale et al. - 1983
9 Output sensitive construction of levels and Voronoi diagrams.. (context) - Mulmuley - 1990
8 On vertical ray-shooting in arrangements (context) - Matousek - 1993
8 New algorithms for minimum area k-gons - Eppstein - 1992
6 a circle placement problem (context) - Chazelle, Lee - 1986
6 Sets without emptyconvex 6-gons - Overmars, Scholten et al. - 1989
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4 The complexity of selection and ranking in X +Y and matrices.. (context) - Frederickson, Johnson - 1982
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