Some directed graph theorems for testing the dynamic full access property of multistage interconnection networks

Fault tolerance of multistage interconnection networks (MINs) has been an important issue for many years. Multiple-pass routing is a technique to make a MIN fault tolerant without adding redundant circuits. The basic idea of multiple-pass routing is to route a packet through a faulty MIN several times, if necessary, until it is delivered to its proper destination. In order to utilize multiple-pass routing schemes, a faulty MIN must possess the dynamic full access (DFA) property. We present a simple procedure for testing the DFA property of a faulty MIN based on a theorem from graph theory. The testing procedure can be applied to find all the subsystems possessing DFA property. Besides, we also introduce the concept of possessing the DFA property within k passes. The shortest path algorithms are applied to check whether or not a faulty MIN possesses the DFA property within k passes.<>