A note on implementing combining networks

In shared-memory multiprocessors, combining networks serve to eliminate hot spots due to concurrent access to the same memory location. Examples are the NYU Ultracomputer, the IBM RP3 and the Fluent Machine. We present a problem that occurs when one tries to implement the Fluent Machine`s network nodes with network chips that do not know their position within the network. We formulate the problem mathematically and present two solutions. The first solution requires some additional hardware around nodes that can be put outside network chips. The second solution requires a minor modification of the routing algorithm, but one can prove that there is no performance loss