Efficient expected-case algorithms for planar point location

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1851, Issue , 2000, Pages 353-366

  Arya, Sunil ^a   Cheng, Siu Wing ^a   Mount, David M ^b   Ramesh, H ^c  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b University of Maryland ^*  (United States)

^c INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; DECISION THEORY; DECISION TREES; ENTROPY; INFORMATION THEORY; PROBABILITY DISTRIBUTIONS; STRUCTURES (BUILT OBJECTS);

DECISION TREE MODELING; LOWER BOUNDS; PLANAR POINT LOCATION; PREPROCESS; QUERY POINTS; QUERY TIME; SEARCH PROBLEM; UNIFORM DISTRIBUTION;

QUERY PROCESSING;

EID: 79960156216     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44985-X     Document Type: Conference Paper

References (22)

1. [1] U. Adamy and R. Seidel. Planar point location close to the information-theoretic lower bound. In Proc. 9th ACM-SIAM Sympos. Discrete Algorithms, 1998.
2. [2] S. Arya and H. Y. Fu. Expected-case complexity of approximate nearest neighbor searching. In Proc. 11th ACM-SIAM Sympos. Discrete Algorithms, pages 379-388, 2000. Extended version appears as HKUST Technical Report HKUST-TCSC-2000-03, URL: http://www.cs.ust.hk/tcsc/RR.
3. [3] M. Bern, D. Eppstein, and S.-H. Teng. Parallel construction of quadtrees and quality triangulations. In Proc. 3rd Workshop Algorithms Data Struct., volume 709 of Lecture Notes in Computer Science, pages 188-199. Springer-Verlag, 1993.
4. [4] P. B. Callahan and S. R. Kosaraju. A decomposition of multi-dimensional pointsets with applications to k-nearest-neighbors and n-body potential fields. In Proc. 24th Ann. ACM Sympos. Theory Comput., pages 546-556, 1992.
5. [5] L. Devroye, E. P. Mücke, and B. Zhu. A note on point location in Delaunay triangulations of random points. Algorithmica, 22:477-482, 1998.
6. [6] D. P. Dobkin and R. J. Lipton. Multidimensional searching problems. SIAM J. Comput., 5:181-186, 1976.
7. [7] M. Edahiro, I. Kokubo, and T. Asano. A new point-location algorithm and its practical efficiency | Comparison with existing algorithms. ACM Trans. Graph., 3(2):86-109, 1984.
8. [8] H. Edelsbrunner, L. J. Guibas, and J. Stolff. Optimal point location in a monotone subdivision. SIAM J. Comput., 15(2):317-340, 1986.
9. [9] K.Y. Fung, T.M. Nicholl, R.E. Tarjan, and C.J. Van Wyk. Simplified linear-time jordan sorting and polygon clipping. Inform. Process. Lett., 35:85-92, 1990.
10. [10] M. T. Goodrich, M. Orletsky, and K. Ramaiyer. Methods for achieving fast query times in point location data structures. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 757-766, 1997.
11. [11] T. C. Hu and A. Tucker. Optimum computer search trees. SIAM J. of Applied Math., 21:514-532, 1971.
12. [12] D. G. Kirkpatrick. Optimal search in planar subdivisions. SIAM J. Comput., 12(1):28-35, 1983.
13. [13] D. E. Knuth. Optimum binary search trees. Acta Informatica, 1:14-25, 1971.
14. [14] D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, Reading, MA, 1973.
15. [15] R. J. Lipton and R. E. Tarjan. Applications of a planar separator theorem. SIAM J. Comput., 9:615-627, 1980.
16. [16] S. Maneewongvatana and D. M. Mount. Analysis of approximate nearest neighbor searching with clustered point sets. In ALENEX, 1999.
17. [17] K. Mehlhorn. Nearly optimal binary search trees. Acta Informatica, 5:287-295, 1975.
18. [18] D. M. Mount and S. Arya. ANN: A library for approximate nearest neighbor searching. 2nd Annual CGC Workshop on Computational Geometry, URL: http://www.cs.umd.edu/~mount/ANN, 1997.
19. [19] E. P. Mücke, I. Saias, and B. Zhu. Fast randomized point location without preprocessing in two-and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274-283, 1996.
20. [20] K. Mulmuley. A fast planar partition algorithm, I. J. Symbolic Comput., 10(3-4):253-280, 1990.
21. [21] N. Sarnak and R. E. Tarjan. Planar point location using persistent search trees. Commun. ACM, 29(7):669-679, July 1986.
22. [22] P. M. Vaidya. An O(n log n) algorithm for the all-nearest-neighbors problem. Discrete Comput. Geom., 4:101-115, 1989.