Power-optimal layout of passive, single-hop, fiber-optic interconnections whose capacity increases with the number of stations

Passive, single-hop interconnections among N stations, each with several transmitters and receivers, provide a communication path between any two stations using one of the transmitters and receivers of each station. Such interconnections which permit a polylogarithmic (in N) number of concurrent transmissions using only spatial separation have previously been described. It is shown how to optimally compose the layouts of any two-fiber-optic single-hop interconnections to form that of the product interconnection. A general method is presented for optimally transforming a layered directed acyclic graph so as to balance the indegree and outdegree of intermediate vertices without altering (source, destination) connectivity