L-infinity interdistance selection by parametric search
Information Processing Letters
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Geometric partitioning made easier, even in parallel
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Proceedings of the eleventh annual symposium on Computational geometry
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Dealing with higher dimensions: the well-separated pair decomposition and its applications
New Techniques for Exact and Approximate Dynamic Closest-point
SIAM Journal on Computing
Two algorithms for nearest-neighbor search in high dimensions
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An Expander-Based Approach to Geometric Optimization
SIAM Journal on 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
A data structure for dynamically maintaining rooted trees
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Average case analysis of dynamic geometric optimization
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Semi-online maintenance of geometric optima and measures
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
High-dimensional computational geometry
High-dimensional computational geometry
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In this paper we present efficient dynamic algorithms for approximation of kth, 1 ≤ k ≤ (n 2) distance defined by some pair of points from a given set S of n points in d-dimensional space, for every fixed d. Our technique is based on dynamization of well-separated pair decomposition proposed in [11], computing approximate nearest and farthest neighbors [23,26] and use of persistent search trees [18].