On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Separators in two and three dimensions
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Separator based parallel divide and conquer in computational geometry
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
Computing a centerpoint of a finite planar set of points in linear time
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On linear-time deterministic algorithms for optimization problems in fixed dimension
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
A 3-space partition and its applications
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Simulating quadratic dynamical systems is PSPACE-complete (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
ACM Computing Surveys (CSUR)
A computational view of population genetics
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Disk packings and planar separators
Proceedings of the twelfth annual symposium on Computational geometry
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
Moments of inertia and graph separators
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Inferring a Union of Halfspaces from Examples
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Multi-dimensional online tracking
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computing a center-transversal line
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Multidimensional online tracking
ACM Transactions on Algorithms (TALG)
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We describe a practical and provably good algorithm forapproximating center points in any number of dimensions. Herec is a center point of a point setP in Rd if every closed halfspace containingc contains at least P/d+1 points of P. Ouralgorithm has a small constant factor and is the first approximatecenter point algorithm whose complexity is subexponential ind. Moreover, it can be optimallyparallelized to require Olog2dloglogn time. Our algorithm has been used in meshpartitioning methods, and has the potential to improve results inpractice for constructing weak &egr;-nets and other geometricalgorithms. We derive a variant of our algorithm with a time bound fullypolynomial in d, and show how tocombine our approach with previous techniques to compute high qualitycenter points more quickly.