Bounds for dispersers, extractors, and depth-two superconcentrators

SIAM Journal on Discrete Mathematics

Volumn 13, Issue 1, 2000, Pages 2-24

  Radhakrishnan, Jaikumar ^a,b   Ta Shma, Amnon ^c,d  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^c INTERNATIONAL COMPUTER SCIENCE INSTITUTE   (United States)

^d WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Dispersers; Entropy loss; Extractors; Superconcentrators

Indexed keywords

EID: 0002956996     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480197329508     Document Type: Article

References (26)

1. N. ALON AND P. PUDLÁK, Superconcentrators of depth 2 and 3; odd levels help (rarely). J. Comput. System Sci., 48 (1994), pp. 194-202.
2. B. BOLLOBAS, Extremal Graph Theory, Academic Press, London, 1978.
3. B. BOLLOBAS, Random Graphs, Academic Press, New York, 1985.
4. B. CHOR AND O. GOLDREICH, Unbiased bits from sources of weak randomness and probabilistic communication complexity, SIAM J. Comput., 17 (1988), pp. 230-261.
5. V. CHVÁTAL, The tail of the hypergeometric distribution, Discrete Math., 25 (1979), pp. 285-287.
6. A. COHEN AND A. WIGDERSON, Dispersers, deterministic amplification and weak random sources, in Proceedings IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamos, CA, 1989, pp. 14-19.
7. D. DOLEV, C. DWORK, N. PIPPENGER, AND A. WIGDERSON, Superconcentrators, generalizers and generalized connectors with limited depth, in Proceedings ACM Symposium on Theory of Computing (STOC), ACM, New York, 1983, pp. 42-51.
8. O. GOLDREICH AND A. WIGDERSON. Tiny families of functions with random properties: A quality-size trade-off for hashing, Random Structures Algorithms, 11 (1997), pp. 315-343.
9. G. HANSEL, Nombre minimal de contacts de fermature nécessaires pour réaliser une fonction booléenne symétrique de n variables, C. R. Acad. Sci. Paris, 258 (1964), pp. 6037-6040.
10. W. HOEFFDING, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc., 58 (1963), pp. 13-30.
11. G. KATONA AND E. SZEMERÉDI, On a problem of graph theory, Studia Sci. Math. Hungar., 2 (1967), pp. 23-28.
12. R. MESHULAM, A geometric construction of a superconcentrator of depth 2, Theoret. Comput. Sci., 32 (1984), pp. 215-219.
13. N. NISAN, Refining randomness: How and why, in Proceedings IEEE Symposium on Computational Complexity, IEEE Computer Society Press, Los Alamitos, CA, 1996, pp 44-58.
14. N. NISAN AND A. WIGDERSON, Research pearls in theory of computation: Homework 2, problem 2; also available online from http://www.cs.huji.ac.il/course/pearls/.
15. N. NISAN AND D. ZUCKERMAN, Randomness is linear in space, J. Comput. System Sci., 52 (1996), pp 43-52.
16. N. PIPPENGER, Superconcentrators, SIAM J. Comput., 6 (1977), pp. 298-304.
17. N. PIPPENGER, Superconcentrators of depth 2, J. Comput. System Sci., 24 (1982), pp 82-90.
18. N. PIPPENGER, Sorting and selecting in rounds, SIAM J. Comput., 16 (1987), pp. 1032-1038.
19. P. PUDLÁK, Communication in bounded depth circuits, Combinatorica, 14 (1994), pp. 203-216.
20. M. SIPSER, Expanders, randomness, or time versus space, J. Comput. System Sci., 36 (1988), pp. 379-383.
21. A. SRINIVASAN AND D. ZUCKERMAN, Computing with very weak random sources, in Proceedings IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 264-275.
22. A. TA-SHMA, Refining Randomness, Ph.D. thesis, The Hebrew University, Jerusalem, 1996.
23. L. VALIANT, Graph-theoretic properties in computational complexity, J. Comput. System Sci., 13 (1976), pp. 278-285.
24. A. WIGDERSON AND D. ZUCKERMAN, Expanders that beat the eigenvalue bound: Explicit construction and applications, in Proceedings ACM Symposium on the Theory of Computing, ACM, New York, 1993, pp. 245-251.
25. D. ZUCKERMAN, Simulating BPP using a general weak random source, Algorithmica, 16 (1996), pp. 367-391.
26. D. ZUCKERMAN, Randomness-optimal oblivious sampling, Random Structures Algorithms, 11 (1997), pp. 345-367.