منابع مشابه
On the Smallest Enclosing Balls
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...
متن کاملFitting the smallest enclosing Bregman balls
Finding a point which minimizes the maximal distortion with respect to a dataset is an important estimation problem that has recently received growing attentions in machine learning, with the advent of one class classification. In this paper, we study the problem from a general standpoint, and suppose that the distortion is a Bregman divergence, without restriction. Applications of this formula...
متن کاملFast and Robust Smallest Enclosing Balls
I describe a C++ program for computing the smallest enclosing ball of a point set in d-dimensional space, using floating-point arithmetic only. The program is very fast for d ≤ 20, robust and simple (about 300 lines of code, excluding prototype definitions). Its new features are a pivoting approach resembling the simplex method for linear programming, and a robust update scheme for intermediate...
متن کاملSmallest Enclosing Disks (balls and Ellipsoids)
A simple randomized algorithm is developed which computes the smallest enclosing disk of a nite set of points in the plane in expected linear time. The algorithm is based on Seidel's recent Linear Programming algorithm, and it can be generalized to computing smallest enclosing balls or ellipsoids of point sets in higher dimensions in a straightforward way. Experimental results of an implementat...
متن کاملEasy and Fast Computation of Approximate Smallest Enclosing Balls
Badoiu and Clarkson [1] introduced an extremely simple incremental algorithm which finds the smallest enclosing ball around points with precision in at most O( ) iteration steps. A simplified proof for this quadratic scaling is given. Based on this proof it is shown that the number of steps in fact increases only like O( ). This new bound leads to a new optimal step size of the algorithm. With ...
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ژورنال
عنوان ژورنال: Communications in Information and Systems
سال: 2006
ISSN: 1526-7555,2163-4548
DOI: 10.4310/cis.2006.v6.n2.a3