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Clos networks are an important class of switching networks due to their modular structure and much lower cost compared with crossbars. For routing I/O permutations of Clos networks, sequential routing algorithms are too slow, and all known parallel algorithms are not practical. We present the algorithm-hardware codesign of a unified fast parallel routing architecture called distributed pipeline routing (DPR) architecture for rearrangeable nonblocking and strictly non-blocking Clos networks. The DPR architecture uses a linear interconnection structure and processing elements that performs only shift and logic AND operations. We show that a DPR architecture can route any permutation in rearrangeable nonblocking and strictly nonblocking Clos networks in OradicN time. The same architecture can be used to carry out control of any group of connection/disconnection requests for strictly nonblocking Clos networks in OradicN time. Several speeding-up techniques are also presented. This architecture is applicable to packet and circuit switches of practical sizes.