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Abstract: We present algorithms for five interdistance enumeration problems that take as input a set S of n points in IR d (for a fixed but arbitrary dimension d) and as output enumerate pairs of points in S satisfying various conditions. We present: an O(n log n + k) time and O(n) space algorithm that takes as additional input a distance # and outputs all k pairs of points in S separated by a distance of # or less; an O(n log n + k log k) time and O(n+k) space algorithm that enumerates in... (Update)
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...n 4 3 , but then the approximation ratio increases. Assume that d # 3. Agarwal, in a personal communication to Dickerson and Eppstein [10], has shown that T sel (n) O(n 2(1 1 (d 1) # ) 7) where # is an arbitrarily small positive real constant. The constant in the Big Oh...
...n 4=3 , but then the approximation ratio increases. Assume that d 3. Agarwal, in a personal communication to Dickerson and Eppstein [10], has shown that T sel (n) O(n 2(1 1= d 1) 7) 21 where is an arbitrarily small positive real constant. The constant in the Big...
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BibTeX entry: (Update)
M.T. Dickerson, D. Eppstein, "Algorithms for proximity problems in higher dimensions", Computational Geometry: Theory and Applications 5, 277--291, 1996. http://citeseer.ist.psu.edu/258426.html More
@article{ dickerson96algorithms,
author = "Matthew T. Dickerson and David Eppstein",
title = "{Algorithms for proximity problems in higher dimensions}",
journal = "Computational Geometry Theory and Applications",
volume = "5",
pages = "277--291",
year = "1996",
url = "citeseer.ist.psu.edu/258426.html" }
Citations (may not include all citations):174 Time bounds for selection (context) - Blum, Floyd et al. - 1973
109 Provably good mesh generation - Bern, Eppstein et al. - 1994
106 A decomposition of multi-dimensional point-sets with applica.. - Callahan, Kosaraju - 1992
94 Closest point problems (context) - Shamos, Hoey - 1975
74 On constructing minimum spanning trees in k-dimensional spac.. (context) - Yao - 1982
67 An unified geometric approach to graph separators (context) - Miller, Teng et al. - 1991
43 Iterated nearest neighbors and finding minimal polytopes - Eppstein, Erickson - 1993
30 Selecting distances in the plane (context) - Agarwal, Aronov et al. - 1990
23 Ambivalent data structures for dynamic 2-edge-connectivity a.. (context) - Frederickson - 1991
22 Simple algorithms for enumerating interpoint distances and f.. (context) - Dickerson, Drysdale et al. - 1992
13 Maintaining the minimal distance of a point set in polylogar.. (context) - Smid - 1991
13 Maintaining the minimal distance of a point set in less than.. (context) - Smid - 1991
11 An optimal algorithm for selection in a min-heap (context) - Frederickson - 1993
11 Optimal parallel all-nearest-neighbors using the well-separa.. - Callahan - 1993
10 On nearest-neighbor graphs (context) - Paterson, Yao - 1992
5 The Complexity of finding fixed-radius near neighbors (context) - Bentley, Stanat et al. - 1977
4 On k-nearest neighbor Voronoi diagrams in the plane (context) - Lee - 1982
3 An O(n log n) algorithm for the all-nearest-neighbors proble.. (context) - Vaidya - 1989
3 Fixed radius search problem for points and segments (context) - Dickerson, Drysdale - 1990
3 Shallow interdistance selection and interdistance enumeratio.. (context) - Salowe - 1991
2 New techniques for computing order statistics in Euclidean s.. (context) - Chazelle - 1985
2 Enumerating k distances for n points in the plane (context) - Dickerson, Drysdale - 1991
2 Enumerating distances in space (context) - Salowe - 1992
2 Enumerating the k closest pairs optimally (context) - Lenhof, Smid - 1992
1 Fast Algorithms for the Greedy Triangulation (context) - Dickerson, Drysdale et al. - 1994
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