1. A method of generating a non-blocking routing network design from a crossbar switch-based network design, the non-blocking routing network design including connections to logic blocks of a programmable integrated circuit, the method comprising: using a programmed processor to perform steps including: determining, for each row of the crossbar switch-based network design, switches in the row that provide switching functions for logically equivalent external connections, the external connections being one of external inputs and external outputs; removing the identified switches from the crossbar switched-based network design; storing information about the identified switches and the logically equivalent external connections for access by a placement module associated with the programmable integrated circuit; accessing the stored information descriptive of the identified switches and the logically equivalent external connections; and placing a logic design within a programmable integrated circuit using the information descriptive of the identified switches and a routing solution.