The power of geometric duality
BIT - Ellis Horwood series in artificial intelligence
Halfspace range search: an algorithmic application of k-sets
Discrete & Computational Geometry
On k-hulls and related problems
SIAM Journal on Computing
Approximate levels in line arrangements
SIAM Journal on Computing
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Data structures for mobile data
Journal of Algorithms
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Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
Lectures on Discrete Geometry
Low-Dimensional Linear Programming with Violations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
SIAM Journal on Computing
Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating extent measures of points
Journal of the ACM (JACM)
On approximating the depth and related problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
How to get close to the median shape
Proceedings of the twenty-second annual symposium on Computational geometry
How to get close to the median shape
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Streaming Algorithms for k-Center Clustering with Outliers and with Anonymity
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Fitting a Step Function to a Point Set
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An Almost Space-Optimal Streaming Algorithm for Coresets in Fixed Dimensions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Processing a large number of continuous preference top-k queries
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Let P be a set of n points in Rd. We show that a (k, ε)-kernel of P of size O(k/ε(d-1)/2) can be computed in time O(n + k2/εd-1), where a (k, ε)-kernel is a subset of P that ε-approximates the directional width of P, for any direction, when k outliers can be ignored in that direction. A (k, ε)-kernel is instrumental in solving shape fitting problems with k outliers, like computing the minimum-width annulus covering all but k of the input points. The size of the new kernel improves over the previous known upper bound O(k/εd-1) [17], and is tight in the worst case. The new algorithm works by repeatedly "peeling" away (0, ε)-kernels. We demonstrate the practicality of our algorithm by showing its empirical performance on various inputs.We also present a simple incremental algorithm for (1 + ε)-fitting various shapes through a set of points with at most k outliers. The algorithm works by repeatedly "grating" critical points into a working set, till the working set provides the required approximation. We prove that the size of the working set is independent of n, and thus results in a simple and practical, near-linear-time algorithm for shape fitting with outliers. We illustrate the versatility and practicality of this technique by implementing approximation algorithms for minimum enclosing circle and minimum-width annulus.