On fault tolerant routings in general networks
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
Incremental Distance and Diameter Sequences of a Graph: New Measures of Network Performance
IEEE Transactions on Computers
Siamese-Twin: A Dynamically Fault-Tolerant Fat-Tree
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
An efficient fault-tolerant routing methodology for fat-tree interconnection networks
ISPA'07 Proceedings of the 5th international conference on Parallel and Distributed Processing and Applications
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We analyze the problem of constructing a network which will have a fixed routing and which will be highly fault tolerant. A construction is presented which forms a “product route graph” from two or more constituent “route graphs.” The analysis involves the surviving route graph, which consists of all non-faulty nodes in the network with two nodes being connected by a directed edge iff the route from the first to the second is still intact after a set of component failures. The diameter of the surviving route graph, that is, the maximum distance between any pair of nodes, is a measure of the worst-case performance degradation caused by the faults. The number of faults tolerated, the diameter, and the degree of the product graph are related in a simple way to the corresponding parameters of the constituent graphs. In addition, there is a “padding theorem” which allows one to add nodes to a graph and to extend a previous routing.