A general framework for developing adaptive fault-tolerant routing algorithms

It is shown that Cartesian product (CP) graph-based network methods provide a useful framework for the design of reliable parallel computer systems. Given component networks with prespecified connectivity, more complex networks with known connectivity and terminal reliability can be developed. CP networks provide systematic techniques for developing reliable fault-tolerant routing schemes, even for very complex topological structures. The authors establish the theoretical foundations that relate the connectivity of a CP network, the connectivity of the component networks, and the number of faulty components: present an adaptive generic algorithm that can perform successful point-to-point routing in the presence of faults: synthesize, using the theoretical results, this adaptive fault-tolerant algorithm from algorithms written for the component networks: prove the correctness of the algorithm: and show that the algorithm ensures following an optimal path, in the presence of many faults, with high probability