Faster core-set constructions and data stream algorithms in fixed dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On approximating the depth and related problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Robust shape fitting via peeling and grating coresets
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Analysis of incomplete data and an intrinsic-dimension Helly theorem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
How to get close to the median shape
Proceedings of the twenty-second annual symposium on Computational geometry
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
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
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
Faster core-set constructions and data-stream algorithms in fixed dimensions
Computational Geometry: Theory and Applications
Extremal point queries with lines and line segments and related problems
Computational Geometry: Theory and Applications
Optimal consensus set for annulus fitting
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Two-Dimensional range diameter queries
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Proceedings of the twenty-ninth annual symposium on Computational geometry
O(n 3logn) time complexity for the optimal consensus set computation for 4-Connected Digital Circles
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Information Processing Letters
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Given a set $\mathcal{H}$ of n hyperplanes in ${\Bbb R}^d$, we present an algorithm that $\eps$-approximates the extent between the top and bottom k levels of the arrangement of $\mathcal{H}$ in time $O(n + (k/\eps)^c)$, where c is a constant depending on d. The algorithm relies on computing a subset of $\mathcal{H}$ of size $O(k/\eps^{d-1})$, 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. These are the first algorithms to handle outliers efficiently for the shape fitting problems considered.