Expanders that beat the eigenvalue bound: Explicit construction and applications

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn Part F129585, Issue , 1993, Pages 245-251

  Wigderson, Avi ^a   Zuckerman, David ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ALGORITHMS; AUTOMATA THEORY; EQUIVALENCE CLASSES; MATRIX ALGEBRA; OPTIMIZATION; RANDOM PROCESSES; SET THEORY;

EIGENVALUE BOUNDS; EXPLICIT CONSTRUCTIONS; MAXIMUM DEGREE; SELECTION ALGORITHM; SORTING ALGORITHM; WIDE SENSE NONBLOCKING;

COMPUTATION THEORY; GRAPH THEORY;

EXPANDER GRAPHS;

EID: 0027306477     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/167088.167163     Document Type: Conference Paper

References (29)

1. [AKS1] M. Ajtai, J. Komlos, and E. Szemeredi, "Sorting in clogn Parallel Steps, " Combi- natorica 3 (1983), pp. 1-19.
2. [AKS2] M. Ajtai, J. Komlos, and E. Szemeredi, "Deterministic Simulation of Logspace, " 19th STOC, 1987, pp. 132-140.
3. [AKSS] M. Ajtai, J. Komlos, W. Steiger, and E. Szemeredi, "Almost Sorting in One Round, " Advances in Computing Research, Vol. 5, 1989, pp. 117-125.
4. [Alol] N. Alon, "Expanders, Sorting in Rounds, and Superconcentrators of Limited Depth, " 17th STOC, 1985, pp. 98-102.
5. [Alo2] N. Alon, "Eigenvalues and Expanders, " Combinatorica 6 (1986), pp. 83-96.
6. [AA] N. Alon and Y. Azar, "Sorting, Approximate Sorting, and Searching in Rounds, " SIAM J. Disc. Math. 1 (1988), pp. 269-280.
7. [AM] N. Alon and V.D. Milman, "Ai, Isoperimet- ric Inequalities for Graphs and Superconcentrators, " J. Combinatorial Theory Ser. B 38 (1985), pp. 73-88.
8. [AP] Y. Azar and N. Pippenger, "Parallel Selection, " Discrete Appl. Math. 27 (1990), pp. 49-58.
9. [BH] B. Bollobas and A. Thomason, "Parallel Sorting, " Discrete Appl. Math. 6 (1983), pp. 1-11.
10. [DDPW] D. Dolev, C. Dwork, N. Pippenger, and A. Wigderson, "Superconcentrators, Generalizes, and Generalized Connectors with Limited Depth, " 15th STOC, 1983, pp. 42-51.
11. [FFP] P. Feldman, J. Friedman, and N. Pippenger, "Wide-Sense Nonblocking Networks, " SIAM J. Disc. Math., 1 (1988), pp. 158-173.
12. [GG] O. Gabber and Z. Galil, "Explicit Construction of Linear Sized Superconcentrators, " J. Comp. and Sys. Set 22 (1981), pp. 407-420.
13. [GIL+] O. Goldreich, R. Impagliazzo, L. Levin, R. Venkatesan, and D. Zuckerman, "Security Preserving Amplification of Hardness, " 31st FOCS, 1990, pp. 318-326.
14. [Kah] N. Kahale, "On the Second Eigenvalue and Linear Expansion of Regular Graphs, " 33rd FOCS, 1992, pp. 296-303.
15. [LPS] A. Lubotzky, R. Philips, P. Sarnak, "Ra- manujan Graphs, " Cornbinaiortca 8 (1988), pp. 261-277.
16. [Mar] G.A. Margulis, "Explicit Construction of Concentrators, " Problems of Inform. Transmission, pp. 325-332.
17. [Mes] R. Meshulam, "A Geometric Construction of a Superconcentrator of Depth 2, " Theoretical Computer Science 32 (1984), pp. 215219.
18. [Mor] M. Morgenstern, "Explicit Construction of Natural Bounded Concentrators, " 32nd FOCS, 1991, pp. 392-397.
19. [NZ] N. Nisan and D. Zuckerman, "More Deterministic Simulation in Logspace, " STOC, 1993, to appear.
20. [Pipl] N. Pippenger, "Superconcentrators, " SIAM J. Comput. 6 (1977), pp. 298-304.
21. [Pip2] N. Pippenger, "Superconcentrators of Depth 2, " J. Comp. and Sys. Sci. 24 (1982), pp. 8290.
22. [Pip3] N. Pippenger, "Sorting and Selecting in Rounds, " SIAM J. Comput. 16 (1987), pp. 1032-1038.
23. [PY] N. Pippenger and A.C. Yao, "Rearrangeable Networks with Limited Depth, " SIAM J. Algebraic and Discrete Methods 3 (1982), pp. 411-417.
24. [Tan] R.M. Tanner, "Explicit Construction of Concentrators from Generalized N-gons, " SIAM J. Alg. Discr. Meth. 5 (1984), pp. 287293.
25. [Tom] M. Tompa, "Time Space Tradeoffs for Computing Functions, Using Connectivity Properties of Their Circuits, " J. Comp. and Sys. Sci, 20 (1980), pp. 118-132.
26. [Vail] L.G. Valiant, "Parallelism in Comparison Problems, " SIAM J. Comput. 4 (1975), pp. 348-355.
27. [Val2] L.G. Valiant, "Graph Theoretic Properties in Computational Complexity, " J. Comp. and Sys. Sci. 13 (1976), pp. 278-285.
28. [Zucl] D. Zuckerman, "General Weak Random Sources, " 31st FOCS, 1990, pp. 534-543.
29. [Zuc2] D. Zuckerman, "Simulating BPP Using a General Weak Random Source, " 32nd FOCS, 1991, pp. 79-89.