A simple algorithm for computing the smallest enclosing circle
Information Processing Letters
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
The SR-tree: an index structure for high-dimensional nearest neighbor queries
SIGMOD '97 Proceedings of the 1997 ACM SIGMOD international conference on Management of data
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fast and Robust Smallest Enclosing Balls
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
The smallest enclosing ball of balls: combinatorial structure and algorithms
Proceedings of the nineteenth annual symposium on Computational geometry
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Core Vector Machines: Fast SVM Training on Very Large Data Sets
The Journal of Machine Learning Research
Efficient Algorithms for the Smallest Enclosing Ball Problem
Computational Optimization and Applications
Simpler core vector machines with enclosing balls
Proceedings of the 24th international conference on Machine learning
Computational Geometry: Theory and Applications
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Two Algorithms for the Minimum Enclosing Ball Problem
SIAM Journal on Optimization
Identification and Elimination of Interior Points for the Minimum Enclosing Ball Problem
SIAM Journal on Optimization
A fast deterministic smallest enclosing disk approximation algorithm
Information Processing Letters
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In this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The algorithm is very simple to implement, gives reliable results, and gracefully handles large problem instances in low and high dimensions, as confirmed by both theoretical arguments and empirical evaluation. For example, using a CPU with eight cores, it takes less than two seconds to compute a 1.001-approximation of the smallest enclosing ball of one million points uniformly distributed in a hypercube in dimension 200. Furthermore, the presented approach extends to a more general class of input objects, such as ball sets.