Easy and Fast Computation of Approximate Smallest Enclosing Balls

نویسندگان

  • Thomas Martinetz
  • Amir Madany Mamlouk
چکیده

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 this new step size one can even expect a O( ) scaling.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Computing Core-Sets and Approximate Smallest Enclosing HyperSpheres in High Dimensions∗

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and “coresets”, we have developed (1 + )-approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/ ), improving the previo...

متن کامل

Comuting Core-Sets and Approximate Smallest Enclosing HyperSpheres in High Dimensions

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and “core-sets”, we have developed (1 + )approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/ ) , improving the previ...

متن کامل

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 کامل

Approximating Smallest Enclosing Balls with Applications to Machine Learning

In this paper, we first survey prior work for computing exactly or approximately the smallest enclosing balls of point or ball sets in Euclidean spaces. We classify previous work into three categories: (1) purely combinatorial, (2) purely numerical, and (3) recent mixed hybrid algorithms based on coresets. We then describe two novel tailored algorithms for computing arbitrary close approximatio...

متن کامل

Smallest 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004