Creating disjoint paths in Gamma interconnection networks

The Gamma interconnection network (GIN) is composed of 3×3 basic building blocks, with interconnecting patterns between stages following the plus-minus-2ⁱ functions. The authors consider modifications to the GIN by altering the interconnecting patterns between stages so as to achieve high terminal reliability between any source-destination pair, resulting in the reliable GIN (REGIN). A type of REGIN´s ensures totally disjoint paths in existence from any source to any destination, thereby capable of tolerating an arbitrary single fault. If several building blocks (i.e., 3×3 switches) are fabricated in one chip with very large scale integrated (VLSI) technology, the layout area and the pin count are less for the REGIN than for its GIN counterpart as a result of the change in the interconnecting patterns, giving rise to potential cost reduction. The terminal reliability of the REGIN is derived and compared with that of a compatible GIN. In addition, the performance of the REGIN is evaluated using simulation