Planar point location in sublogarithmic time

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2006, Pages 325-332

  Pǎtraşcu, Mihai ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; DATA STRUCTURES; DISTRIBUTED COMPUTER SYSTEMS; QUERY PROCESSING;

BOUNDED UNIVERSE; SUBLOGARITHMIC QUERY; SUBLOGARITHMIC TIME;

PROBLEM SOLVING;

EID: 34250344286     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2006.61     Document Type: Conference Paper

References (27)

1. S. Alstrup, T. Husfeldt, and T. Rauhe. A cell probe lower bound for dynamic nearest-neighbor searching. In Proc 12th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 779-780, 2001.
2. A. Amir, A. Efrat, P. Indyk, and H. Samet. Efficient regular data structures and algorithms for dilation, location, and proximity problems. Algorithmica, 30(2): 164-187, 2001.
3. See also FOCS'99.
4. A. Andersson. Faster deterministic sorting and searching in linear space. In Proc 37th IEEE Symposium on Foundations of Computer Science (FOCS), pages 135-141, 1996.
5. S. Arya, T. Malamatos, and D. M. Mount. Entropy-preserving cuttings and space-efficient planar point location. In Proc 20th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 256-261, 2001.
6. S. Arya, T. Malamatos, and D. M. Mount. A simple entropy-based algorithm for planar point location. In Proc 20th ACM/SIAM Symposium on Discrete Algorithms (SODA), pages 262-268, 2001.
7. T. M. Chan. Point location in o(log n) time, Voronoi diagrams in o(n log n) time, and other transdichotomous results in computational geometry. In Proc 47th IEEE Symposium on Foundations of Computer Science (FOCS), 2006.
8. R. Cole. Searching and storing similar lists. Journal of Algorithms, 7(2):202-220, 1986.
9. M. de Berg, M. J. van Kreveld, and J. Snoeyink. Two-and three-dimensional point location in rectangular subdivisions. Journal of Algorithms, 18(2):256-277, 1995. See also SWAT'92.
10. D. P. Dobkin and R. J. Lipton. Multidimensional searching problems. SIAM Journal on Computing, 5(2):181-186, 1976.
11. H. Edelsbrunner, L. J. Guibas, and J. Stolfi. Optimal point location in a monotone subdivision. SIAM Journal on Computing, 15(2):317-340, 1986.
12. M. L. Fredman and D. E. Willard. Surpassing the information theoretic bound with fusion trees. Journal of Computer and System Sciences, 47(3):424-436, 1993. See also STOC'90.
13. Y. Han. Deterministic sorting in o(n log log n) time and linear space. Journal of Algorithms, 50(1):96-105, 2004. See also STOC'02.
14. Y. Han and M. Thorup. Integer sorting in 0(n√log log n) expected time and linear space. In Proc 43rd IEEE Symposium on Foundations of Computer Science (FOCS), pages 135-144, 2002.
15. J. Iacono. Expected asymptotically optimal planar point location. Computational Geometry, 29(1):19-22, 2004. See also SODA'01.
16. J. Iacono and S. Langerman. Dynamic point location in fat hyperrectangles with integer coordinates. In Proc 12th Canadian Conference on Computational Geometry (CCCG), 2000.
17. D. G. Kirkpatrick. Optimal search in planar subdivisions. SIAM Journal on Computing, 12(1):28-35, 1983.
18. R. J. Lipton and R. E. Tarjan. Applications of a planar separator theorem. SIAM Journal on Computing, 9(3):615-627, 1980.
19. See also FOCS'77.
20. K. Mulmuley. A fast planar partition algorithm. Journal of Symbolic Computation, 10(3/4):253-280, 1990.
21. See also FOCS'88.
22. M. Pǎtraşcu and M. Thorup. Time-space trade-offs for predecessor search. In Proc 38th ACM Symposium on Theory of Computing (STOC), pages 232-240, 2006.
23. N. Sarnak and R. E. Tarjan. Planar point location using persistent search trees. Communications of the ACM, 29(7):669-679, 1986.
24. R. Seidel and U. Adamy. On the exact worst case query complexity of planar point location. Journal of Algorithms, 37(1): 189-217, 2000.
25. See also SODA'98.
26. J. Snoeyink. Point location. In J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry (2nd edition), pages 767-785. Chapman & Hall/CRC, 2004.
27. P. van Emde Boas, R. Kaas, and E. Zijlstra. Design and implementation of an efficient priority queue. Mathematical Systems Theory, 10:99-127, 1977. Announced by van Emde Boas alone at FOCS'75.