Analysis of link traffic in incomplete hypercubes

A variation of the hypercube, called the incomplete hypercube, allows any sized construction, providing for better incremental flexibility. In this paper, traffic density over links in an incomplete hypercube with arbitrary size is analyzed for the first time. Despite its structural non-homogeneity, an incomplete hypercube is shown to exhibit bounded link traffic density (i.e., ⩽ 2 messages per link per cycle) under the uniform message distribution, independent of the system size. As a result, it is easily achievable to build an incomplete hypercube with sufficient link communication capability that avoids any potential points of congestion, ensuring high performance. The incomplete hypercube thus appears to be an attractive and practical candidate topology for interconnecting parallel systems, since it shares every advantage of complete hypercubes while eliminating the restriction on system sizes