Deterministic many-to-many hot potato routing

We consider algorithms for many-to-many hot potato routing. In hot potato (deflection) routing, a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for many-to-many packet routing in commonly occurring networks such as the hypercube, meshes, and tori of various dimensions and sizes, trees, and hypercubic networks such as the butterfly. All these algorithms are analyzed using a charging scheme that may be applicable to other algorithms as well. Moreover, all bounds hold in a dynamic setting in which packets can be injected at arbitrary times.