Approximating the diameter of a set of points in the Euclidean space
Information Processing Letters
A subexponential bound for linear programming
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
Self-scaled barriers and interior-point methods for convex programming
Mathematics of Operations Research
An efficient, exact, and generic quadratic programming solver for geometric optimization
Proceedings of the sixteenth annual symposium on Computational geometry
Approximating the diameter, width, smallest enclosing cylinder, and minimum-width annulus
Proceedings of the sixteenth annual symposium on Computational geometry
Randomizing combinatorial algorithms for linear programming when the dimension is moderately high
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Reductions among high dimensional proximity problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Warm-Start Strategies in Interior-Point Methods for Linear Programming
SIAM Journal on Optimization
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Choosing Multiple Parameters for Support Vector Machines
Machine Learning
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
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
The Journal of Machine Learning Research
Computational Geometry: Theory and Applications
Analysis of incomplete data and an intrinsic-dimension Helly theorem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithms for two-box covering
Proceedings of the twenty-second annual symposium on Computational geometry
Multiclass core vector machine
Proceedings of the 24th international conference on Machine learning
Simpler core vector machines with enclosing balls
Proceedings of the 24th international conference on Machine learning
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Computational Geometry: Theory and Applications
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Enclosing Machine Learning for Class Description
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks
ISNN '08 Proceedings of the 5th international symposium on Neural Networks: Advances in Neural Networks
From minimum enclosing ball to fast fuzzy inference system training on large datasets
IEEE Transactions on Fuzzy Systems
Hierarchical Core Vector Machines for Network Intrusion Detection
ICONIP '09 Proceedings of the 16th International Conference on Neural Information Processing: Part II
Bounded-hop energy-efficient broadcast in low-dimensional metrics via coresets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Minimum-energy broadcast with few senders
DCOSS'07 Proceedings of the 3rd IEEE international conference on Distributed computing in sensor systems
Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm
ACM Transactions on Algorithms (TALG)
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Ordinal-class core vector machine
Journal of Computer Science and Technology
Minimal containment under homothetics: a simple cutting plane approach
Computational Optimization and Applications
Flexible aggregate similarity search
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
INFORMS Journal on Computing
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Instant approximate 1-center on road networks via embeddings
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Training minimum enclosing balls for cross tasks knowledge transfer
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part I
A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems
Computational Optimization and Applications
Streaming and dynamic algorithms for minimum enclosing balls in high dimensions
Computational Geometry: Theory and Applications
Fast classification for large data sets via random selection clustering and Support Vector Machines
Intelligent Data Analysis
Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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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 + ε)-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/ε), improving the previous bound of O(1/ε2), and we study empirically how the core-set size grows with dimension. We show that our algorithm, which is simple to implement, results in fast computation of nearly optimal solutions for point sets in much higher dimension than previously computable using exact techniques.