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We have previously proposed an efficient switch architecture called multiple input/output-queued (MIOQ) switch and showed that the MIOQ switch can match the performance of an output-queued switch statistically. In this paper, we prove theoretically that the MIOQ switch can match the output queueing exactly , not statistically, with no speedup of any component. More specifically, we show that the MIOQ switch with two parallel switches (which we call a parallel MIOQ (PMIOQ) switch in this paper) can provide exact emulation of an output-queued switch with a broad class of service scheduling algorithms including FIFO, weighted fair queueing (WFQ) and strict priority queueing regardless of incoming traffic pattern and switch size. To do that, we first propose the stable strategic alliance (SSA) algorithm that can produce a stable many-to-many assignment, and prove its finite, stable and deterministic properties. Next, we apply the SSA algorithm to the scheduling of a PMIOQ switch with two parallel switches, and show that the stability condition of the SSA algorithm guarantees for the PMIOQ switch to emulate an output-queued switch exactly. To avoid possible conflicts in a parallel switch, each input-output pair matched by the SSA algorithm must be mapped to one of two crossbar switches. For this mapping, we also propose a simple algorithm that requires at most 2N steps for all matched input-output pairs. In addition, to relieve the implementation burden of N input buffers being accessed simultaneously, we propose a buffering scheme called redundant buffering which requires two memory devices instead of N physically-separate memories. In conclusion, we demonstrate that the MIOQ switch requires two crossbar switches in parallel and two physical memories at each input and output to emulate an output-queued switch with no speedup of any component.