Computational geometry: an introduction
Computational geometry: an introduction
Optimal point location in a monotone subdivision
SIAM Journal on Computing
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the complexity of some geometric problems in unbounded dimension
Journal of Symbolic Computation
Out-of-Roundness Problem Revisited
IEEE Transactions on Pattern Analysis and Machine Intelligence
Applications of parametric searching in geometric optimization
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
A complete roundness classification procedure
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing Envelopes in Four Dimensions with Applications
SIAM Journal on Computing
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Projective clustering in high dimensions using core-sets
Proceedings of the eighteenth annual symposium on Computational geometry
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
Efficient Randomized Algorithms for Some Geometric Optimization
Efficient Randomized Algorithms for Some Geometric Optimization
SIAM Journal on Computing
Discrete & Computational Geometry
Approximating extent measures of points
Journal of the ACM (JACM)
High-Dimensional Shape Fitting in Linear Time
Discrete & Computational Geometry
Proceedings of the twenty-fourth annual symposium on Computational geometry
Proceedings of the forty-first annual ACM symposium on Theory of computing
A unified framework for approximating and clustering data
Proceedings of the forty-third annual ACM symposium on Theory of computing
A near-linear algorithm for projective clustering integer points
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Data reduction for weighted and outlier-resistant clustering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Net and prune: a linear time algorithm for euclidean distance problems
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We show that coresets do not exist for the problem of 2-slabs in ${\mathbb R}^{3}$, thus demonstrating that the natural approach for solving approximately this problem efficiently is infeasible. On the positive side, for a point set P in ${\mathbb R}^{3}$, we describe a near linear time algorithm for computing a (1+ε)-approximation to the minimum width 2-slab cover of P. This is a first step in providing an efficient approximation algorithm for the problem of covering a point set with k-slabs.