منابع مشابه
On the Smallest Enclosing Information Disk
In this paper, we present a generalization of the smallest enclosing disk problem for point sets lying in Information-geometric spaces. Given a set of vector points equipped with a (dis)similarity measure that is not necessarily the Euclidean distance, we investigate the problem of finding its center defined as the point minimizing the maximum distance to the point set. For a broad class of dis...
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In the paper a theoretical analysis is given for the smallest ball that covers a finite number of points p1, p2, · · · , pN ∈ R . Several fundamental properties of the smallest enclosing ball are described and proved. Particularly, it is proved that the k-circumscribing enclosing ball with smallest k is the smallest enclosing ball, which dramatically reduces a possible large number of computati...
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Let S be a set of n points in the plane. We present a method where, using O(n log n) time and space, S can be pre-processed into a data structure such that given an axis-parallel query rectangle q, we can report the radius of the smallest enclosing disk of the points lying in S ∩ q in O(log n) time per query.
متن کاملA fast deterministic smallest enclosing disk approximation algorithm
We describe a simple and fast O(n log2 1 ε )-time algorithm for finding a (1 + ε)-approximation of the smallest enclosing disk of a planar set of n points or disks. Experimental results of a readily available implementation are presented. 2004 Elsevier B.V. All rights reserved.
متن کاملApproximating smallest enclosing disks
#"%$'&( *) -time algorithms were designed for the planar case in the early 1970s [4, 6], the problem complexity was only settled in 1984 with N. Megiddo’s first linear time algorithm [3] for solving linear programs in fixed dimension. Unfortunately, these algorithms exhibit a large constant hidden in the big-Oh notation and do not perform so well in practice. E. Welzl [8] developed a simple rec...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2008
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2007.08.007