Traffic analysis and simulation performance of incomplete hypercubes

The incomplete hypercube with arbitrary nodes provides far better incremental flexibility than the complete hypercube, whose size is restricted to exactly a power of 2. After faults arise in a complete hypercube system, it is desirable to reconfigure the system so as to retain as many healthy nodes as possible, often leading to an incomplete hypercube of arbitrary size. In this paper, the highest traffic density over links in an incomplete hypercube under uniform message distribution is shown to be bounded by 2 (messages per link per cycle), independent of its size and despite its structural nonhomogeneity. As a result, it is easily achievable to construct an incomplete hypercube with sufficient link communication capability where any potential points of congestion are avoided, ensuring high performance. Simulation results for the incomplete hypercube reveal that mean latency for delivering messages is roughly the same in an incomplete hypercube as in a compatible complete hypercube under both packet-switching and wormhole routing. The incomplete hypercube thus appears to be an attractive and practical architecture, since it shares every advantage of complete hypercubes while eliminating the restriction on the system size.