Optimum embeddings of end-around meshes into pyramid networks

To increase the utility of task-oriented or specialized parallel networks, especially those already constructed, one can simulate one parallel network on another. Of primary interest then is the lower bound on the cost of such a simulation. The authors show that end-around meshes can be mapped to pyramids with dilation two, and minimal expansion. Furthermore, they show that if all computations are synchronized using a global clock, one can achieve an effective edge congestion of one. In this manner, they remove the need for scheduling or queueing of messages since each communication link hosts at most one message path per cycle. Hence, they obtain essentially a contention-free simulation of one parallel interconnection network by another. They also prove that this embedding is optimum, i.e. end-around meshes are not subgraphs of pyramids