Fast, deterministic routing, on hypercubes, using small buffers

A deterministic routing scheme for a communications network based on the k-dimensional hypercube is proposed. The author presents two formulations of the scheme. The first formulation delivers messages in O(k²) bit times using O(K ) bits of buffer space at each node in the hypercube. The second formulation assumes that there are several batches of messages to be delivered, and makes certain assumptions about the cost of sending messages along the various dimensions of the cube. In this case, the latency for delivery time is still O(k²) bit times, but the throughput is increased to one set of messages every O(k) bit times. For the first formulation, the author restricts himself to routings which are subsets of permutations (i.e. every node sends at most one message and receives at most one message). The second formulation indicates a way to perform routings which are subsets of H-permutations (i.e. every node sends at most H messages and receives at most H messages)