Fault-tolerance analysis of multistage interconnection networks with fixed control values

In this paper, the routing capability in multistage interconnection networks is formulated as a Boolean matrix of control variables. Simple procedures for computing this matrix and how to modify it for a given fault set are illustrated. This formulation is used to investigate a new fault-tolerant routing property. The new property, namely, dynamic-fault-accessibility with fixed control values (DFA-FC) deals with the capability of establishing all node-to-node connections via multiple passes through the network to circumvent faulty switches in the original routes. A faulty network possesses the DFA-FC property if A node-to-node connections can be established via multiple passes using fixed control values for all passes and connections. The DFA-FC property provides a simple and fast routing mechanism in contrast to the already known property the dynamic-fault-accessibility with changeable control values (DFA-CC). The symmetric group theory is utilized to prove a necessary and sufficient condition for the DFA-FC property. Based on this condition, a procedure for testing this property is devised. For the property DFA-CC, a new necessary and sufficient condition is proven. This new condition provides an efficient testing procedure of this property for any multistage interconnection networks.