Approximating probability distributions using small sample spaces

Combinatorica

Volumn 18, Issue 2, 1998, Pages 151-171

  Azar, Yossi ^a   Motwani, Rajeev ^c   Naor, Joseph ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^c Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040350285     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009813     Document Type: Article

References (28)

1. N. ALON, O. GOLDREICH, J. HÅSTAD, and R. PERALTA: Simple Constructions of Almost k-wise Independent Random Variables, Random Structures and Algorithms, 3 (1992), 289-304.
2. N. ALON, L. BABAI, and A. ITAI: A fast and simple randomized parallel algorithm for the maximal independent set problem, Journal of Algorithms, 7 (1986), 567-583.
3. N. ALON and J. SPENCER: The Probabilistic Method, John Wiley, 1992.
4. L. BABAI: Fourier Transforms and Equations over Finite Abelian Groups, Lecture Notes, University of Chicago, 1989.
5. E. BACH and J. SORENSON: Explicit Bounds for Primes in Residue Classes, Mathematics of Computation, 65 (1996), 1717-1735.
6. R. BEN-NATHAN: On dependent random variables over small sample spaces, M.Sc. Thesis, Hebrew University, Jerusalem, Israel (1990).
7. c n)-wise independence in NC, Journal of the ACM, 38 (1991), 1026-1046.
8. B. CHOR and O. GOLDREICH: On the power of two-point based sampling, Journal of Complexity, 5 (1989), 96-106.
9. B. CHOR, O. GOLDREICH, J. HÅSTAD, J. FRIEDMAN, S. RUDICH, and R. SMOLENSKY: t-Resilient functions, In Proceedings of the 26th Annual Symposium on the Foundations of Computer Science (1985), 396-407.
10. H. DAVENPORT: Multiplicative Number Theory, 2nd Edition, Springer Verlag, 1980.
11. H. DYM and H. P. MCKEAN: Fourier Series and Integrals, Academic Press, 1972.
12. P. ERDÖS and J. SELFRIDGE: On a combinatorial game, J. Combinatorial Theory, Ser. B, 14 (1973), 298-301.
13. P. ERDÖS and J. SPENCER: Probabilistic Methods in Combinatorics, Akadémiai Kiadó, Budapest, 1974.
14. T. ESTERMANN: Introduction to Modern Prime Number Theory, Cambridge University Press, 1969.
15. G. EVEN: Construction of small probability spaces for deterministic simulation, M.Sc. Thesis, Technion, Haifa, Israel (1991).
16. J. HÅSTAD, S. PHILLIPS, and S. SAFRA: A Well Characterized Approximation Problem, In Proceedings of the 2nd Israel Symposium on Theory and Computing Systems (1993), 261-265.
17. D. R. HEATH-BROWN: Zero-Free Regions for Dirichlet L-Functions and the Least Prime in an Arithmetic Progression, Proc. London Math. Soc. 64 (1991), 265-338.
18. R. M. KARP and A. WIGDERSON: A Fast Parallel Algorithm for the Maximal Independent Set Problem, Journal of the ACM, 32 (1985), 762-773.
19. T. W. KÖRNER: Fourier Analysis, Cambridge University Press (1988).
20. W. LEDERMANN: Introduction to Group Characters, Cambridge University Press (1987, 2nd edition).
21. M. LUBY: A simple parallel algorithm for the maximal independent set, SIAM Journal on Computing, 15 (1986), 1036-1053.
22. M. LUBY: Removing randomness in parallel computation without a processor penalty, In Proceedings of the 29th Annual Symposium on Foundations of Computer Science (1988), 162-173.
23. R. MOTWANI, J. NAOR, and M. NAOR: The probabilistic method yields deterministic parallel algorithms, Journal of Computer and System Sciences, 49 (1994), 478-516.
24. F. J. MACWILLIAMS and N. J. A. SLOANE: The Theory of Error Correcting Codes, North-Holland (1977).
25. J. NAOR and M. NAOR: Small-bias probability spaces: efficient constructions and applications, SIAM Journal on Computing, 22 (1993), 838-856.
26. R. PERALTA: On the randomness complexity of algorithms, CS Research Report TR 90-1, University of Wisconsin, Milwaukee (1990).
27. W. M. SCHMIDT: Equations over Finite Fields: An Elementary Approach, Lecture Notes in Mathematics, v. 536, Springer-Verlag (1976).
28. U. VAZIRANI: Randomness, Adversaries and Computation, Ph.D. Thesis, University of California, Berkeley (1986).