Solving some discrepancy problems in NC

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

Volumn 1346, Issue , 1997, Pages 22-36

  Mahajan, Sanjeev ^a   Ramos, Edgar A ^b   Subrahmanyam, K V ^c  

^a AGERE SYSTEMS   (United States)

^b MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^c SPIC Mathemat Institute   (India)

Author keywords

[No Author keywords available]

Indexed keywords

SOFTWARE ENGINEERING;

EDGE-COLORING OF GRAPHS; GEOMETRIC CONFIGURATIONS; INTEGER LINEAR PROGRAMS; LATTICE APPROXIMATIONS; MULTIPLICATIVE FACTORS; PROBABILISTIC ANALYSIS; PROBABILISTIC BOUNDS; RANGE SPACES;

INTEGER PROGRAMMING;

EID: 0005258732     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0058020     Document Type: Conference Paper

References (32)

1. N. Alon and J. Spencer. The Probabilistic Method. Wiley-Interscience, 1992.
2. N. Alon and A. Srinivasan. Improved parallel approximation of a class of integer programming problems. Algorithmica 17 (1997) 449-462.
3. N. M. Amato, M. T. Goodrich, and E. A. Ramos. Parallel algorithms for higherdimensional convex hulls. In Proc. 35th Annu. IEEE Sympos. Found. Comput. Sci., 1994, 683-694.
4. N. M. Amato, M. T. Goodrich, and E. A. Ramos. Computing faces in segment and simplex arrangements. In Proc. 27th Annu. ACM Sympos. Theory Comput., 1995, 672-682.
5. J. Beck and W. Chen. Irregularities of distribution. Cambridge University Press, 1987.
6. M. Bellare and J. Rompel. Randomness-efficient oblivious sampling. In Proc. 35th Annu. IEEE Sympos. Found. Comput. Sci., 1994, 276-287.
7. c n)-wise independence in NC. Journal ACM 38 (1991) 1026-1046.
8. S. Chari, P. Rohatgi and A. Srinivasan. Improved Algorithms via Approximations of Probability Distributions. In Proc. ACM Sympos. Theory Comput. (1994) 584-592.
9. B. Chazelle and J. Friedman. A deterministic view of random sampling and its use in geometry. Combinatorica 10 (1990) 229-249.
10. B. Chazelle and J. Matousek. On linear-time deterministic algorithms for optimization problems in fixed dimension. In Proc. 4th ACM-SIAM Sympos. Discrete Algorithms, pages 281-290, 1993.
11. H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics 23 (1952) 493-509.
12. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4 (1989) 387-421.
13. M.T. Goodrich. Geometric partitioning made easier, even in parallel. In Proc. 9th Annu. ACM Sympos. Comput. Geom., 73-82, 1993.
14. M.T. Goodrich. Fixed-dimensional parallel linear programming via relative ε-approximations. In Proc. 7th ACM-SIAM Sympos. Discr. Alg. (SODA), 1996, 132-141.
15. M.T. Goodrich and E.A. Ramos. Bounded independence derandomization of geometric partitioning with applications to parallel fixed-dimensional linear programming. To appear in Discrete and Comput. Geom.
16. W. Hoeffding. Probability inequalities for sums of bounded random variables. American Statist. Assoc. J. 58 (1963) 13-30.
17. A. Joffe. On a set of almost deterministic k-independent random variables. Annals of Probability 2 (1974) 161-162.
18. D.R. Karger and D. Roller. (De)randomized constructions of small sample spaces in NC. In Proc. 35th Annu. IEEE Sympos. Foundations Comput. Sci., 1994, 252-263.
19. H.J. Karloff and Y. Mansour. On construction of k-wise independent random variables. In Proc. 26th Annu. ACM Sympos. Theory Comput., 1994, 564-573.
20. H.J. Karloff and D.B. Shmoys. Efficient parallel algorithms for edge coloring problems. 3. Algorithms 8 (1987) 39-52.
21. M. Luby and N. Nisan. A parallel approximation algorithm for positive linear programming. In Proc. 25th Annu. ACM Sympos. Theory Comput., 1993, 448-457.
22. J. Matoušek. Approximations and optimal geometric divide-and-conquer. In Proc. 23rd Annu. ACM Sympos. Theory Comput., 1991, 505-511. Also in J. Comput. Syst. Sci. 50 (1995) 203-208.
23. J. Matoušek. Efficient partition trees. Discrete Comput. Geom. 8 (1992) 315-334.
24. J. Matoušek. Derandomization in computational geometry. Available in the web site: http://www.ms.mff.cuni.cz/acad/kam/matousek/ Earlier version appeared in J. Algorithms.
25. R. Motwani, J. Naor and M. Naor. The probabilistic method yields deterministic parallel algorithms. J. Comput. Syst. Sci. 49 (1994) 478-516.
26. K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, Englewood Cliffs, NJ, 1993.
27. J. Naor and M. Naor. Small-bias probability spaces: efficient constructions and applications. SIAM J. Comput. 22 (1993) 838-856.
28. N. Nisan. Pseudorandom generators for space-bounded computation. Combinatorica 12 (1992) 449-461.
29. P. Raghavan. Probabilistic construction of deterministic algorithms: Approximating packing integer programs. J. Comput. Syst. Sci. 37 (1988) 130-143.
30. P. Raghavan and C.D. Thompson. Randomized rounding: A technique for provably good algorithms and algorithmic proofs. Combinatorica 7 (1987) 365-374.
31. J.P. Schmidt, A. Siegel and A. Srinivasan. Chernoff-Hoeffding bounds for applications with limited independence. SIAM J. Discrete Math. 8 (1995) 223-250.
32. V.N. Vapnik and A.Y. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16 (1971) 264-280.