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Closest-point problems
Abstract
A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straight-line triangulation. For most of the problems considered a lower bound of O(N log N) is shown. For all of them the best currently-known upper bound is O(N2) or worse. The purpose of this paper is to introduce a single geometric structure, called the Voronoi diagram, which can be constructed rapidly and contains all of the relevant proximity information in only linear space. The Voronoi diagram is used to obtain O(N log N) algorithms for all of the problems.
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Cited by
Approximate nearest neighbors: towards removing the curse of dimensionality
Indyk, P., & Motwani, R. (1998) · Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98 · doi:10.1145/276698.276876 · Cited by 4,188
On the shape of a set of points in the plane
Edelsbrunner, H., Kirkpatrick, D., & Seidel, R. (1983) · IEEE Transactions on Information Theory · doi:10.1109/tit.1983.1056714 · Cited by 1,634
Generalized delaunay triangulation for planar graphs
Lee, D. T., & Lin, A. K. (1986) · Discrete & Computational Geometry · doi:10.1007/bf02187695 · Cited by 286
Demonstrating the Transferability and the Descriptive Power of Sketch-Map
Ceriotti, M., Tribello, G. A., & Parrinello, M. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct3010563 · Cited by 126
Metadata
- Authors
- Shamos, M. I., & Hoey, D.
- Venue
- 16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
- Publisher
- IEEE
- Published
- 1975-10
- Pages
- 151-162
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2007610503
- Cited by
- 1,057
- References
- 0
- FWCI
- 6.40
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Shamos, M. I., & Hoey, D. (1975). Closest-point problems. 16th Annual Symposium on Foundations of Computer Science (sfcs 1975). https://doi.org/10.1109/sfcs.1975.8
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