Product range spaces, sensitive sampling, and derandomization

SIAM Journal on Computing

Volumn 28, Issue 5, 1999, Pages 1552-1575

  Brönnimann, Hervé ^a   Chazelle, Bernard ^b   Matoušek, Jiří ^c  

^a INRIA   (France)

^b Princeton University   (United States)

^c CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; GEOMETRY; PROBABILITY; RANDOM PROCESSES; SAMPLING; SET THEORY;

CONVEX HULL; DETERMINISTIC ALGORITHM; PRODUCT RANGE SPACES;

APPROXIMATION THEORY;

EID: 0344210448     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539796260321     Document Type: Article

References (24)

1. A. V. AHO, J. E. HOPCROFT, AND J. D. ULLMAN, Data Structures and Algorithms, Addison-Wesley, Reading, MA, 1983.
2. N. ALON AND J. SPENCER, The Probabilistic Method, John Wiley & Sons, New York, 1992.
3. N. AMATO, M. GOODRICH, AND E. RAMOS, Parallel algorithms for higher-dimensional convex hulls, in Proc. 35th Annu. IEEE Sympos. Found. Comput. Sci., Santa Fe, NM, 1994, pp. 683-694.
4. N. AMATO, M. GOODRICH, AND E. RAMOS, Computing faces in segment and simplex arrangements, in Proc. 27th ACM Symp. Theor. Comput., Las Vegas, NV, 1995, pp. 672-682.
5. H. BRÖNNIMANN, Derandomization of Geometric Algorithms, Ph.D. thesis, Dept. of Comput. Sci., Princeton University, Princeton, NJ, 1995.
6. B. CHAZELLE, Cutting hyperplanes for divide-and-conquer, Discrete Comput. Geom., 9 (1993), pp. 145-158.
7. B. CHAZELLE, An optimal convex hull algorithm in any fixed dimension. Discrete Comput. Geom., 10 (1993), pp. 377-409.
8. B. CHAZELLE, H. EDELSBRUNNER, M. GRIGNI, L. J. GUIBAS, AND M. SHARIR, Improved bounds on weak ε-nets for convex sets. Discrete Comput. Geom., 13, (1995), pp. 1-15.
9. B. CHAZELLE AND J. FRIEDMAN, A deterministic view of random sampling and its use in geometry, Combinatorica, 10 (1990), pp. 229-249.
10. B. CHAZELLE AND J. MATOUŠEK On linear-time deterministic algorithms for optimization problems infixed dimension, J. Algorithms, 21 (1996), pp. 579-597.
11. K. L. CLARKSON, A randomized algorithm for closest-point queries, SIAM J. Comput., 17 (1988), pp. 830-847.
12. K. L. CLARKSON, Randomized Geometric Algorithms, in Computing in Euclidean Geometry, Lecture Notes Series Comput. 1, D.-Z. Du, F. K. Kwang. eds., World Scientific, River Edge, NJ, 1992, pp. 117-162.
13. K. L. CLARKSON AND P. W. SHOR, Applications of random sampling in computational geometry, II, Discrete Comput. Geom., 4 (1989), pp. 387-421.
14. R. M. DUDLEY AND R. S. WENOCUR, Some special Vapnik-Chervonenkis classes, Discrete Math., 33 (1981), pp. 313-318.
15. H. EDELSBRUNNER, Algorithms in Combinatorial Geometry, Springer-Verlag, New York, 1987.
16. H. EDELSBRUNNER AND E. P. MÜCKE, Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms, ACM Trans. Graph., 2 (1990), pp. 66-104.
17. D. HAUSSLER AND E. WELZL, ε-nets and simplex range queries, Discrete Comput. Geom., 2 (1987), pp. 127-151.
18. J. MATOUŠEK, Construction of ε-nets, Discrete Comput. Georn., 5 (1990), pp. 427-448.
19. J. MATOUŠEK, Cutting hyperplane arrangements, Discrete Comput. Geom., 6 (1991), pp. 385-406.
20. J. MATOUŠEK, Approximations and optimal geometric divide-and-conquer, J. Comput. System Sci., 50 (1995), pp. 203-208.
21. J. MATOUŠEK, Efficient partition trees, Discrete Comput. Geom., 8 (1992), pp. 315-334.
22. H. NIEDERREITER, Random Number Generation and Quasi Monte-Carlo Methods, CBMS-NSF 63, SIAM, Philadelphia, PA, 1992.
23. P. RAGHAVAN, Probabilistic construction of deterministic algorithms: Approximating packing integer programs, J. Comput. System Sci., 37 (1988), pp. 130-143.
24. J. SPENCER, Ten Lectures on the Probabilistic Method, CBMS-NSF, SIAM, Philadelphia, PA, 1987.