Filtering search: a new approach to query answering
SIAM Journal on Computing
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Minimum spanning trees in k-dimensional space
SIAM Journal on Computing
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
Lower bounds for orthogonal range searching: part II. The arithmetic model
Journal of the ACM (JACM)
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Range searching with efficient hierarchical cuttings
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Handbook of discrete and computational geometry
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Dynamic algorithms for geometric spanners of small diameter: randomized solutions
Computational Geometry: Theory and Applications
ACM SIGACT News
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
Dynamic Data Structures for Realtime Management of Large Geormetric Scences (Extended Abstract)
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Sublinear geometric algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Estimating the weight of metric minimum spanning trees in sublinear-time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Sampling in dynamic data streams and applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Online geometric reconstruction
Proceedings of the twenty-second annual symposium on Computational geometry
Scalable multicasting with network-aware geometric overlay
Computer Communications
Online geometric reconstruction
Journal of the ACM (JACM)
Research paper: The saga of minimum spanning trees
Computer Science Review
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We consider the problem of finding the weight of a Euclidean minimum spanning tree for a set of n points in ℝd. We focus on the situation when the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within 1 + ε using only Õ(√ poly(1/ε)) queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbors queries.