Fault tolerance and generalization on a class of multistage interconnection networks

Benes networks are known as the non-blocking rearrangeable networks which can realize arbitrary permutation without conflict. In this thesis, a class of 2$log\sb bN$ stage rearrangeable networks which are equivalent to Benes networks is introduced. Networks in this class can be either symmetric or asymmetric in their structure, regular or irregular in their inter-stage connections, and $2log\sb bN$ or 2$log\sb bN -$ 1 stages. A switch labelling scheme is proposed to provide means for testing the topological and functional equivalency for this class of networks. This switch labelling scheme can also provide a novel matrix representation for network configuration. This new representation introduces a portability concept for the routing scheme on this class of networks. With this new representation, a general routing scheme is also developed which can realize arbitrary permutation for the whole class of 2$log\sb bN$ stage networks. In this thesis, we also propose two types of general fault-tolerant routing schemes for the whole class of $2log\sb2 N$ stage networks: First, a one-pass fault-tolerant routing scheme is presented. For the failure of control line in the switches, a fault-free routing algorithm is proposed to tolerate multiple faults on each stage of the network. For the failure of switch data lines and inter-stage links, a graceful degradation routing algorithm is developed to configure the network so that the loss is ensured to be minimal for weighted permutation requests. Second, a novel two-pass fault-tolerant routing scheme is proposed to tolerate more switch and link faults when one-pass fault-tolerant routing fails. Our two-pass fault-tolerant routing scheme dramatically increases the fault-tolerant capability of a network. It can tolerate the failure of almost half of a network.