Algorithms for Proximity Problems in Higher Dimensions (1996)
| Venue: | Comput. Geom. Theory Appl |
| Citations: | 22 - 2 self |
BibTeX
@ARTICLE{Dickerson96algorithmsfor,
author = {Matthew Dickerson and David Eppstein},
title = {Algorithms for Proximity Problems in Higher Dimensions},
journal = {Comput. Geom. Theory Appl},
year = {1996},
volume = {5},
pages = {277--291}
}
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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 non-decreasing order the k closest pairs of points in S; an O(n log n + k) time algorithm for the same problem without any order restrictions; an O(nk log n) time and O(n) space algorithm that enumerates in nondecreasing order the nk pairs representing the k nearest neighbors of each point in S; and an O(n log n + kn) time algorithm for the same problem without any order restrictions. The algorithms combine a modification of the planar approach of Dickerson, Drysdale, and Sack [11] with the ...
