Expanders that beat the eigenvalue bound: Explicit construction and applications

Combinatorica

Volumn 19, Issue 1, 1999, Pages 125-138

  Wigderson, Avi ^b   Zuckerman, David ^a  

^a University of Texas at Austin   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040707391     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004930050049     Document Type: Article

References (32)

1. M. AJTAI, J. KOMLÓS, and E. SZEMERÉDI: Sorting in clog n parallel steps, Combinatorica, 3 (1983), 1-19.
2. M. AJTAI, J. KOMLÓS, and E. SZEMERÉDI: Deterministic simulation of Logspace, in Proceedings of the 19th Annual ACM Symposium on Theory of Computing, 1987, 132-140.
3. M. AJTAI, J. KOMLÓS, W. STEIGER, and E. SZEMERÉDI: Almost sorting in one round, Advances in Computing Research, 5 (1989), 117-125.
4. N. ALON: Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory, Combinatorica, 6 (1986), 207-219.
5. N. ALON: Eigenvalues and expanders, Combinatorica, 6 (1986), 83-96.
6. N. ALON and Y. AZAR: Sorting, approximate sorting, and searching in rounds, SIAM J. Disc. Math., 1 (1988), 269-280.
7. 1, isoperimetric inequalities for graphs and superconcentrators, J. Combin. Theory Ser. B, 38 (1985), 73-88.
8. Y. AZAR and N. PIPPENGER: Parallel selection, Discrete Appl. Math., 27 (1990), 49-58.
9. B. BOLLOBÁS and A. THOMASON: Parallel sorting, Discrete Appl. Math., 6 (1983), 1-11.
10. D. DOLEV, C. DWORK, N. PIPPENGER, and A. WIGDERSON: Superconcentrators, generalizes, and generalized connectors with limited depth, in Proceedings of the 19th Annual ACM Symposium on Theory of Computing, 1983, 42-51.
11. P. FELDMAN, J. FRIEDMAN, and N. PIPPENGER: Wide-sense nonblocking networks, SIAM J. Disc. Math., 1 (1988), 158-173.
12. O. GABBER and Z. GALIL: Explicit construction of linear sized superconcentrators, J. Comp. and Sys. Sci, 22 (1981), 407-420.
13. O. GOLDREICH, R. IMPAGLIAZZO, L. LEVIN, R. VENKATESAN, and D. ZUCKERMAN: Security preserving amplification of hardness, in Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, 1990, 318-326.
14. N. KAHALE: Eigenvalues and expansion of regular graphs, Journal of the ACM, 42 (1995), 1091-1106.
15. A. LUBOTZKY, R. PHILIPS, P. SARNAK: Ramanujan graphs, Combinatorica, 8 (1988), 261-277.
16. G.A. MARGULIS: Explicit construction of concentrators, Problems of Inform. Transmission, 325-332.
17. R. MESHULAM: A geometric construction of a superconcentrator of depth 2, Theoretical Computer Science, 32 (1984), 215-219.
18. M. MORGENSTERN: Explicit construction of natural bounded concentrators, in Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, 1991, 392-397.
19. N. NISAN and D. ZUCKERMAN: Randomness is linear in space, Journal of Computer and System Sciences, 52 (1996), 43-52.
20. N. PIPPENGER: Superconcentrators, SIAM J. Comput., 6 (1977), 298-304.
21. N. PIPPENGER: Superconcentrators of depth 2, J. Comp. and Sys. Sci., 24 (1982), 82-90.
22. N. PIPPENGER: Sorting and selecting in rounds, SIAM J. Comput., 16 (1987), 1032-1038.
23. N. PIPPENGER and A.C. YAO: Rearrangeable networks with limited depth, SIAM J. Alg. Discr. Meth., 3 (1982), 411-417.
24. A. SRINIVASAN and D. ZUCKERMAN: Computing with very weak random sources, in Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, 1994, 264-275. To appear in SIAM Journal on Computing.
25. R.M. TANNER: Explicit construction of concentrators from generalized N-gons, SIAM J. Alg. Discr. Meth., 5 (1984), 287-293.
26. A. TA-SHMA: On extracting randomness from weak random sources, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing, 1996, 276-285.
27. M. TOMPA: Time space tradeoffs for computing functions using connectivity properties of their circuits, J. Comp. and Sys. Sci, 20 (1980), 118-132.
28. L.G. VALIANT: Parallelism in comparison problems, SIAM J. Comput., 4 (1975), 348-355.
29. L.G. VALIANT: Graph theoretic properties in computational complexity, J. Comp. and Sys. Sci., 13 (1976), 278-285.
30. D. ZUCKERMAN: General weak random sources, in Proceedings of the 31st Annual IEEE Symposium on Foundations of Computer Science, 1990, 534-543.
31. D. ZUCKERMAN: Simulating BPP using a general weak random source, Algorithmica, 16 (1996), 367-391.
32. D. ZUCKERMAN: Randomness-optimal oblivious sampling, Random Structures and Algorithms, 11 (1997), 345-367.