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This paper presents a novel approach to reducing the communication costs incurred when performing multiple multicasts on wormhole routed two-dimensional mesh multiprocessor systems. Both unicast and path-based implementations of multicasting incur communication costs due to the inherent message passing and contention for network resources. The start-up time dominates the transmission time when the data volume is small. However, in the presence of multiple multicasts when the data volume is very large, the communication delays due to message blocking and resource contention become very significant. Because of this, we present a hybrid static-dynamic technique to reduce the communication costs incurred when performing multiple multicasts on wormhole routed direct networks. This technique requires a focus on ordering and routing information for the individual message transmissions. At compile time, each message is assigned a priority using the recently developed collision graph model. Then at runtime these priorities are used to arbitrate the message transmissions. As a base, dimension-ordered routing is used. However, to further reduce the communication costs, some messages will be rerouted. This technique is useful either as a stand-alone algorithm or as an embedded procedure into existing algorithms. Furthermore, the techniques can be applied to higher dimension direct networks. For a single multicast, our work performs as well as conventional methods. For multiple multicasts, results show that our approach provides significant improvement over baseline techniques.