This paper provides necessary and sufficient conditions for deadlock-free unicast and multicast routing with the path-based routing model in interconnection networks which use the wormhole switching technique. The theory is developed around three central concepts: channel waiting, false resource cycles, and valid destination sets. The first two concepts are suitable extensions to those developed for unicast routing by two authors of this paper; the third concept has been developed by Lin and Ni. The necessary and sufficient conditions can be applied in a straightforward manner to prove deadlock freedom and to find more adaptive routing algorithms for collective communication. The latter point is illustrated by developing two routing algorithms for multicast communication in 2-D mesh architectures. The first algorithm uses fewer resources (channels) than an algorithm proposed in the literature but achieves the same adaptivity. The second achieves full adaptivity for multicast routing.
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