Expanders that beat the eigenvalue bound: Explicit construction and applications (Q1125612)

Improving the extractor construction of Nisan and Zuckerman a Log-space algorithm is presented that on input \(n\) and \(0<\delta<1\) constructs \(n^\delta\)-expanding graphs on \(n\) nodes with maximum degree \(n^{1-\delta+o(1)}\). The following applications are given: a \(k\)-round sorting algorithm using \(n^{1+1/k+o(1)}\) comparisons; a \(k\)-round selection algorithm using \(n^{1+1/(2^k-1)+o(1)}\) comparisons; a depth 2 superconcentrator of size \(n^{1+o(1)}\); and a depth \(k\) wide-sense nonblocking generalized connector of size \(n^{1+1/k+o(1)}\).