Expanders that beat the eigenvalue bound: explicit construction and applications

@inproceedings{Wigderson1993ExpandersTB,
title={Expanders that beat the eigenvalue bound: explicit construction and applications},
author={Avi Wigderson and David Zuckerman},
booktitle={STOC},
year={1993}
}

For every n and O < ii < 1, we construct graphs on n nodes such that every two sets of size n* share an edge, having essentially optimal maximum degree ~1–~+0(1). Wfe use them to explicitly con.!?. trUCt: 1. A k round sorting algorithm using nl+li~+”(l) comparisons. 2. A k round selection algorithm using ~l+l/(Zk-l)+O(l) comparisons. 3. A depth 2 superconcentrator of size nl+”(l). 4. A depth k wide-sense nonblocking generalized connector of size nl+llk+O(l ). All of these results improve on… CONTINUE READING