Expanders That Beat the Eigenvalue Bound: Explicit Construction and Applications


and 0 < δ < 1, we construct graphs on n nodes such that every two sets of size share an edge, having essentially optimal maximum degree . Using known and new reductions from these graphs, we derive new explicit constructions of:

1.  A k round sorting algorithm using comparisons.

2.  A k round selection algorithm using comparisons.

3.  A depth 2 superconcentrator of size .

4.  A depth k wide-sense nonblocking generalized connector of size .

All of these results improve on previous constructions by factors of , and are optimal to within factors of . 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.

This is a preview of subscription content, access via your institution.

Author information



Additional information

Received: June 13, 1995/Revised: Revised October 23, 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wigderson, A., Zuckerman, D. Expanders That Beat the Eigenvalue Bound: Explicit Construction and Applications. Combinatorica 19, 125–138 (1999). https://doi.org/10.1007/s004930050049

Download citation


  • Explicit Construction