Methods of design directional-coupler-based switching networks with minimum number of crossovers are presented. Also presented is a modular construction scheme that allows large switching networks (with minimum of crossovers) to be built using identical chips containing smaller networks of the same type. The total number of crossovers and the maximum number of crossovers between an inlet-outlet pair have been analyzed in three major self-routing networks. Since many networks are based on these topologies, the results can be applied extensively to the study of many other switching networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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