Optimal Fully Adaptive Minimal Wormhole Routing for Meshes

A deadlock-free fully adaptive minimal routing algorithm for meshes that is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. It is also proved that, ignoring symmetry, this routing algorithm is the only fully adaptive routing algorithm with uniform routers that achieves both of these goals. This new algorithm requires only virtual channels for an -dimensional mesh. In addition, if more than the minimum number of virtual channels is available, the routing algorithm can use these additional channels with the fewest possible number of restrictions. The proofs are first presented for the 2D mesh and then generalized to -dimensional meshes.