## Expanders that Beat the Eigenvalue Bound: Explicit Construction and Applications (1993)

Venue: | Combinatorica |

Citations: | 89 - 26 self |

### BibTeX

@ARTICLE{Wigderson93expandersthat,

author = {Avi Wigderson and David Zuckerman},

title = {Expanders that Beat the Eigenvalue Bound: Explicit Construction and Applications},

journal = {Combinatorica},

year = {1993},

volume = {19},

pages = {245--251}

}

### Years of Citing Articles

### OpenURL

### 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 generalized connector of size n 1+1=k+o(1) . All of these results improve on previous constructions by factors of n\Omega\Gamma37 , and are optimal to within factors of n o(1) . These results are based on an improvement to the extractor construction of Nisan & Zuckerman: our algorithm extracts an asymptotically optimal number of random bits from a defective random source using a small additional number of truly random bits. 1