Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On enclosing k points by a circle
Information Processing Letters
Static and dynamic algorithms for k-point clustering problems
Journal of Algorithms
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Maintaining approximate extent measures of moving points
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Optimal outlier removal in high-dimensional
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Low-Dimensional Linear Programming with Violations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximate Shape Fitting via Linearization
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the least median square problem
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximating extent measures of points
Journal of the ACM (JACM)
A practical approximation algorithm for the LMS line estimator
Computational Statistics & Data Analysis
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Given a set H of n hyperplanes in Rd, we present an algorithm that e-approximates the extent between the top and bottom k levels of the arrangement of H in time O(n + (k/e)c), where c is a constant depending on d. The algorithm relies on computing a subset of H of size.O(k/ed-1), in near linear time, such that the k-level of the arrangement of the subset approximates that of the original arrangement. Using this algorithm, we propose efficient approximation algorithms for shape fitting with outliers for various shapes. This is the first algorithms to handle outliers efficiently for the shape fitting problems considered.