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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
[Article contains additional citations not shown here]
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