Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
A Subexponential Algorithm for Abstract Optimization Problems
SIAM Journal on Computing
Data structures for mobile data
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An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithms for a Minimum Volume Enclosing Simplex in Three Dimensions
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for k-Line Center
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Proceedings of the nineteenth annual symposium on Computational geometry
Approximating extent measures of points
Journal of the ACM (JACM)
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
Proceedings of the twenty-fourth annual symposium on Computational geometry
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Flexible aggregate similarity search
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Lower bounds for number-in-hand multiparty communication complexity, made easy
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Processing a large number of continuous preference top-k queries
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
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The notion of ε-kernel was introduced by Agarwal et al. to set up a unified framework for computing various extent measures of a point set p approximately. Roughly speaking, a subset Q ⊆ P is an ε-kernel of P if for every slab W containing Q, the expanded slab (1+ε)W contains P. They illustrated the significance of an ε-kernel by showing that it yields approximation algorithms for a wide range of problems.We present a simpler and more practical algorithm for computing the ε-kernel of a set P of points in ℝ3. We demonstrate the practicality of our algorithm by showing its empirical performance on various inputs. We then describe an incremental algorithm for fitting various shapes and use the ideas of our algorithm for computing ε-kernels to analyze the performance of this algorithm. We illustrate the versatility and practicality of this technique by implementing approximation algorithms for minimum enclosing cylinder, minimum-volume bounding box, and minimum-width annulus. Finally, we show that ε-kernels can be effectively used to expedite the algorithms for maintaining extents of moving points.