The connection cubes: symmetric, low diameter interconnection networks with low node degree

The enhanced connection cube or ECC and the minimal connection cube or MCC, proposed in this paper, are regular and symmetric static interconnection networks for large-scale, loosely coupled systems. The ECC connects 2²ⁿ⁺¹ processing nodes with only n+2 links per node, almost half the number used in a comparable hypercube. Yet its diameter is only n+2, almost half that of the hypercube. The MCC connects 2²ⁿ⁺¹ nodes using only n+1 links per node, has about the same diameter as a hypercube and is scalable like the hypercube. The MCC can be converted into the ECC by adding one more link per node. Both networks can emulate all the connections present in a hypercube of the same size, with no increase in routing complexity, so that typical parallel applications run on both types of CCs with the same time complexity as on a hypercube