Farthest neighbors, maximum spanning trees and related problems in higher dimensions
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Maintaining approximate extent measures of moving points
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A practical approach for computing the diameter of a point set
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Space-efficient approximate Voronoi diagrams
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Introduction to Algorithms
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Penetration depth of two convex polytopes in 3D
Nordic Journal of Computing
Better algorithms for high-dimensional proximity problems via asymmetric embeddings
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
High-dimensional shape fitting in linear time
Proceedings of the nineteenth annual symposium on Computational geometry
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
SIAM Journal on Computing
Practical methods for shape fitting and kinetic data structures using core sets
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Adaptive sampling for geometric problems over data streams
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Geometric optimization problems over sliding windows
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
A space-optimal data-stream algorithm for coresets in the plane
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Hausdorff approximation of 3D convex polytopes
Information Processing Letters
Proceedings of the twenty-fourth annual symposium on Computational geometry
Enclosing weighted points with an almost-unit ball
Information Processing Letters
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We speed up previous (1 + ε)-factor approximation algorithms for a number of geometric optimization problems in fixed dimensions: diameter, width, minimum-radius enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc. Linear time bounds were known before; we further improve the dependence of the "constants" in terms of ε.We next consider the data-stream model and present new (1 + ε)-factor approximation algorithms that need only constant space for all of the above problems in any fixed dimension. Previously, such a result was known only for diameter.Both sets of results are obtained using the core-set framework recently proposed by Agarwal, Har-Peled, and Varadarajan. Published by Elsevier B.V.