J. S. Salowe, "Enumerating distances in space", International Journal of Computational Geometry and Applications, 2:1 (1992) 49--59. Home/Search Document Not in Database Summary Related Articles Check |
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Algorithms for Proximity Problems in Higher Dimensions - Dickerson, Eppstein (1996) (10 citations) (Correct)
....of points may lie within a given distance of each other. The problem was originally solved by Bentley, Stanat, and Williams [5] in worst case time O(3 d dn log n 3 d k) where d is the dimension and k the number of pairs reported. Algorithms for problem 1 have also been used by Salowe [21, 22] and Lenhof and Smid [17] as subroutines in parametric search methods for solving Problems 2 and 4. Problem 3 is a generalization of the well known nearest neighbors problem. For classification problems, it is more robust than a simple nearest neighbors search. The graph of k nearest neighbors to ....
....# is any arbitrarily small constant. Salowe has also solved the interdistance selection problem for the L # metric in d dimensions in O(n log d n) time [20] for k # n, and has since extended these results to get an O(n log n k) time algorithm for Problem 2 that works for any L p metric [21, 22]; however the value of k must be known in advance, and the distances are not enumerated in order. As a sub step, Salowe also presents an algorithm to solve Problem 1, the fixed radius nearneighbor search problem, in time O(n log n k) for L p metrics in d dimensions. This algorithm was inspired by ....
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J. S. Salowe, "Enumerating distances in space", International Journal of Computational Geometry and Applications, 2:1 (1992) 49--59.
Fast Greedy Triangulation Algorithms - Dickerson, Drysdale, McElfresh.. (1994) (14 citations) (Correct)
.... it generates possible edges in increasing order using an algorithm of Dickerson, Drysdale, and Sack [8] Algorithms to enumerate the k closest interpoint pairs have been invented by Salowe and by Lenhof and Smid, but because they need to know k in advance they are less appropriate in this context [32, 17]. When the number of pairs of not closed points is proportional to the number of pairs already examined, it starts over, enumerating pairs of not closed points in increasing order (similar to Step 2 0 above) How do we know when to switch over We keep track of the number of points which are ....
J.S. Salowe, "Enumerating distances in space." Internat. J. Comput. Geometry Appl. 2 (1992) 49--59
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