1. A multiplexer-based network for providing routing equivalence to a non-blocking crossbar network that has a plurality of crossbar switches making up an ingress stage, a middle stage, and an egress stage, wherein the non-blocking crossbar network includes a plurality of crossbar rows, each crossbar row including outbound and inbound internal connections to another crossbar row, the multiplexer-based network comprising: a plurality of multiplexer-based network rows, each multiplexer-based network row of the plurality of multiplexer-based network rows corresponding to a crossbar row of the non-blocking crossbar network and including: at least one global input, at least one global output, a plurality of internal inputs, a plurality of internal outputs, and a set of multiplexers, wherein the set of multiplexers includes: an internal multiplexer for each respective internal output of the respective crossbar row, the internal multiplexer including a set of inputs coupled to signals routable to the respective outbound internal connection of the respective crossbar row, and at least one global multiplexer providing a signal to a global output of the multiplexer-based network row, the global multiplexer including a set of inputs that includes each input of the respective crossbar row.