Size-depth tradeoff for strictly non-blocking generalized-concentrators

The study of interconnection networks is relevant to theoretical computer science in areas such as parallel computations, graph pebbling, oblivious computations for many naturally occurring functions, modeling circuits with limited depth and unbounded fan-in, and implementation on parallel computers of algorithms for sorting. In this paper, we study the size-depth complexity tradeoff for strictly non-blocking generalized-concentrators. Our motivation for studying the size-depth tradeoffs for concentrators and generalized-concentrators derives from considering the gap between the lower and upper size bounds versus depth for connectors and generalized-connectors, in the strictly non-blocking context. Concentrators have been used as basic subnetworks in designing other species of networks such as rearrangeable superconcentrators and generalized concentrators, and wide-sense non-blocking generalized-connectors. These size-depth tradeoffs for concentrators and generalized-concentrators may provide an insight into using these networks as principal components in designing other strictly non-blocking networks.