Disjoint path properties of the data manipulator network family

A critical component of any parallel processing system is the interconnection network that provides communications among the system's processors and memories. The data manipulator (gamma) network family is an important class of multistage interconnection networks that is being studied by various researchers. One interesting property of the data manipulator network family is the existence of multiple paths through the network for most source/ destination pairs. The condition that must be present to have disjoint paths through the network for a given source/ destination pair is shown, where disjoint paths are multiple paths with no links in common. It is derived that the maximum number of disjoint paths for any source/destination pair is two and a method for finding the routing tags that specify these paths is given. For source/destination pairs that have disjoint paths, a single fault cannot prevent communication between that source/ destination pair. The effect of a fault in a given stage of the network on the number of source/destination pairs that can be connected is also discussed. All results are proven mathematically.