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Abstract: For every n and 0 ! ffi ! 1, we construct graphs on n nodes such that every two sets of size n ffi share an edge, having essentially optimal maximum degree n 1\Gammaffi+o(1) . Using known and new reductions from these graphs, we explicitly construct: 1. A k round sorting algorithm using n 1+1=k+o(1) comparisons. 2. A k round selection algorithm using n 1+1=(2 k \Gamma1)+o(1) comparisons. 3. A depth 2 superconcentrator of size n 1+o(1) . 4. A depth k wide-sense nonblocking... (Update)
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BibTeX entry: (Update)
A. Wigderson, D. Zuckerman, " Expanders that Beat the Eigenvalue Bound, Explicit Construction and Applications", Proc. of the 25th STOC, pp. 245--251, 1993. To appear in Combinatorica. http://citeseer.ist.psu.edu/wigderson93expanders.html More
@inproceedings{ wigderson93expanders,
author = "Avi Wigderson and David Zuckerman",
title = "Expanders that beat the eigenvalue bound: explicit construction and applications",
pages = "245--251",
year = "1993",
url = "citeseer.ist.psu.edu/wigderson93expanders.html" }
Citations (may not include all citations):148 Ramanujan Graphs (context) - Lubotzky, Philips et al. - 1988
126 Eigenvalues and Expanders (context) - Alon - 1986
88 Deterministic Simulation of Logspace (context) - Ajtai, Komlos et al. - 1987
84 Simulating BPP Using a General Weak Random Source - Zuckerman - 1996
79 Parallelism in Comparison Problems (context) - Valiant - 1975
75 Randomness is Linear in Space - Nisan, Zuckerman - 1996
71 Explicit Construction of Linear Sized Superconcentrators (context) - Gabber, Galil - 1981
60 Computing with Very Weak Random Sources - Srinivasan, Zuckerman - 1994
54 Explicit Construction of Concentrators (context) - Margulis
36 Randomness-Optimal Oblivious Sampling - Zuckerman - 1997
36 Security Preserving Amplification of Hardness - Goldreich, Impagliazzo et al. - 1990
35 On Extracting Randomness from Weak Random Sources (context) - Ta-Shma - 1996
35 General Weak Random Sources (context) - Zuckerman - 1990
29 Sorting and Selecting in Rounds (context) - Pippenger - 1987
21 Explicit Construction of Concentrators from Generalized N-go.. (context) - Tanner - 1984
20 Eigenvalues and expansion of regular graphs - Kahale - 1995
20 Graph Theoretic Properties in Computational Complexity (context) - Valiant - 1976
17 Sorting in c log n Parallel Steps (context) - Ajtai, Komlos et al. - 1983
17 Wide-Sense Nonblocking Networks (context) - Feldman, Friedman et al. - 1988
13 1 , Isoperimetric Inequalities for Graphs and Superconcentra.. (context) - Alon, Milman - 1985
11 A Geometric Construction of a Superconcentrator of Depth 2 (context) - Meshulam - 1984
9 Rearrangeable Networks with Limited Depth (context) - Pippenger, Yao - 1982
9 Almost Sorting in One Round (context) - Ajtai, Komlos et al. - 1989
8 Eigenvalues, Geometric Expanders, Sorting in Rounds, and Ram.. (context) - Alon - 1986
7 Superconcentrators (context) - Pippenger - 1977
5 Superconcentrators, Generalizers, and Generalized Connectors.. (context) - Dolev, Dwork et al. - 1983
4 Time Space Tradeoffs for Computing Functions, Using Connecti.. (context) - Tompa - 1980
3 Explicit Construction of Natural Bounded Concentrators (context) - Morgenstern - 1991
3 Superconcentrators of Depth 2 (context) - Pippenger - 1982
3 Parallel Selection (context) - Azar, Pippenger - 1990
2 Sorting, Approximate Sorting, and Searching in Rounds (context) - Alon, Azar - 1988
2 Parallel Sorting (context) - Bollobas, Thomason - 1983
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