Computational geometry: an introduction
Computational geometry: an introduction
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Approximating the diameter of a set of points in the Euclidean space
Information Processing Letters
Point location in arrangements of hyperplanes
Information and Computation
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Locality-preserving hashing in multidimensional spaces
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Subquadratic approximation algorithms for clustering problems in high dimensional spaces
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximating matrix multiplication for pattern recognition tasks
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Greedy strikes back: improved facility location algorithms
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for a capacitated facility location problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Locally lifting the curse of dimensionality for nearest neighbor search (extended abstract)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Dimensionality reduction techniques for proximity problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On Computing the Diameter of a Point Set in High Dimensional Euclidean Space
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
On Approximate Nearest Neighbors in Non-Euclidean Spaces
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Divide-and-conquer in multidimensional space
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
High-dimensional computational geometry
High-dimensional computational geometry
An O (N2.5) algorithm for maximum matching in general graphs
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Derandomized dimensionality reduction with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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
Quick k-Median, k-Center, and Facility Location for Sparse Graphs
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Distributed self-stabilizing placement of replicated resources in emerging networks
IEEE/ACM Transactions on Networking (TON)
Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
The string edit distance matching problem with moves
ACM Transactions on Algorithms (TALG)
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Efficient approximation algorithms for clustering point-sets
Computational Geometry: Theory and Applications
Streaming algorithms for extent problems in high dimensions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
No dimension independent core-sets for containment under homothetics
Proceedings of the twenty-seventh annual symposium on Computational geometry
Geometric optimization problems over sliding windows
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Bottleneck non-crossing matching in the plane
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Bottleneck non-crossing matching in the plane
Computational Geometry: Theory and Applications
Fast and robust approximation of smallest enclosing balls in arbitrary dimensions
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present improved running times for a wide range of approximate high dimensional proximity problems. We obtain subquadratic running time for each of these problems. These improved running times are obtained by reduction to Nearest Neighbour queries. The problems we consider in this paper are Approximate Diameter, Approximate Furthest Neighbours, Approximate Discrete Center, Approximate Metric Facility Location, Approximate Bottleneck Matching, and Approximate Minimum Weight Matching.