From expanders to better superconcentrators without cascading

Abstract

Superconcentration is a strong property of interconnection diagraphs. We characterize its negation by existence of two disjoint and seperated sets which shrink under the forward and backward neighbor relation, respectively. This enables a better, non-cascaded design of superconcentrators, explicit ones with edge density ≤ 118, random ones with edge density ≤ 13.