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Optimal Search in Planar Subdivisions
Abstract
A planar subdivision is any partition of the plane into (possibly unbounded) polygonal regions. The subdivision search problem is the following: given a subdivision S with n line segments and a query point P, determine which region of S contains P . We present a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely $O(\log n)$ search time with $O(n)$ storage. Our subdivision search structure can be constructed in linear time from the subdivision representation used in many applications.
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Citations
Cited by
Mitchell, J. S. B., Mount, D. M., & Papadimitriou, C. H. (1987) · SIAM Journal on Computing · doi:10.1137/0216045 · Cited by 720
Generalized delaunay triangulation for planar graphs
Lee, D. T., & Lin, A. K. (1986) · Discrete & Computational Geometry · doi:10.1007/bf02187695 · Cited by 286
Metadata
- Authors
- Kirkpatrick, D.
- Venue
- SIAM Journal on Computing
- Published
- 1983-02
- Volume
- 12
- Issue
- 1
- Pages
- 28-35
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2126876121
- Cited by
- 739
- References
- 0
- FWCI
- 39.53
- Type
- journal article
- Language
- en
- Open access
- closed
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- Kirkpatrick, D. (1983). Optimal Search in Planar Subdivisions. SIAM Journal on Computing. https://doi.org/10.1137/0212002
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
