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Nowadays, scalability, parallelism and fault-tolerance are key features to take advantage of last silicon technology advances, and that is why reconfigurable architectures are in the spotlight. However, one of the major problems in designing reconfigurable and parallel processing elements concerns the design of a cost-effective interconnection network. This way, considering that Multistage Interconnection Network (MIN) has been successfully used in several computer system levels and applications in the past, in this work we propose the use of a MIN, at the word level, on a coarse-grained reconfigurable architecture. More precisely, this work presents a novel parallel self-placement and routing mechanism for MIN on the circuit-switching mode. We take into account one-to-one as well as multicast (one-to-many) permutations. Our approach is scalable and it is targeted to be used in run-time environments where dynamic routing among functional units is required. In addition, our algorithm is embedded in the switch structure, and it is independent of the interstage interconnection pattern. Our approach can handle blocking and non-blocking networks, symmetrical or asymmetrical topologies. As case study, we use the proposed technique in a dynamic reconfigurable system, showing a major area reduction of 30% without performance overhead.