ISSN:
1432-0541
Keywords:
Key words. Spatial decomposition, Computational geometry, Closest pair, n -Body problem.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. In this paper we show that if the input points to the geometric closest pair problem are given with limited precision (each coordinate is specified with O( log n) bits), then we can compute the closest pair in O(n log log n) time. We also apply our spatial decomposition technique to the k -nearest neighbor and n -body problems, achieving similar improvements. To make use of the limited precision of the input points, we use a reasonable machine model that allows ``bit shifting'' in constant time—we believe that this model is realistic, and provides an interesting way of beating the Ω(n log n) lower bound that exists for this problem using the more typical algebraic RAM model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s004530010040
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