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<p><it>Abstract</it>—A theory for the design of deadlock-free adaptive routing algorithms for wormhole networks was proposed in [<ref rid="BIBD097612" type="bib">12</ref>], [<ref rid="BIBD097616" type="bib">16</ref>]. This theory supplies the sufficient conditions for an adaptive routing algorithm to be deadlock-free, even when there are cyclic dependencies between channels. Also, two design methodologies were proposed. Multicast communication refers to the delivery of the same message from one source node to an arbitrary number of destination nodes. A tree-like routing scheme is not suitable for hardware-supported multicast in wormhole networks because it produces many headers for each message, drastically increasing the probability of a message being blocked. A path-based multicast routing model was proposed in [<ref rid="BIBD097625" type="bib">25</ref>] for multicomputers with 2D-mesh and hypercube topologies. In this model, messages are not replicated at intermediate nodes. This paper develops the theoretical background for the design of deadlock-free adaptive multicast routing algorithms. This theory is valid for wormhole networks using the path-based routing model. It is also valid when messages with a single destination and multiple destinations are mixed together. The new channel dependencies produced by messages with several destinations are studied. Also, two theorems are proposed, developing conditions to verify that an adaptive multicast routing algorithm is deadlock-free, even when there are cyclic dependencies between channels. As an example, the multicast routing algorithms presented in [<ref rid="BIBD097625" type="bib">25</ref>] are extended, so that they can take advantage of the alternative paths offered by the network.</p>
Adaptive routing, deadlock avoidance, graph theory, multicast routing, multicomputers, path-based multicast, virtual channels, wormhole routing.

J. Duato, "A Theory of Deadlock-Free Adaptive Multicast Routing in Wormhole Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 976-987, 1995.
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