Fault-Tolerant Routing in Multistage Interconnection Networks
IEEE Transactions on Computers
Interpolation between bases and the shuffle exchange network
European Journal of Combinatorics
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
CGIN: A Fault Tolerant Modified Gamma Interconnection Network
IEEE Transactions on Parallel and Distributed Systems
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Adding Multiple-Fault Tolerance to Generalized Cube Networks
IEEE Transactions on Parallel and Distributed Systems
The Palindrome Network for Fault-Tolerant Interconnection
SPDP '96 Proceedings of the 8th IEEE Symposium on Parallel and Distributed Processing (SPDP '96)
Fault-tolerant cube graphs and coding theory
IEEE Transactions on Information Theory - Part 2
A Fault-Tolerant Rearrangeable Permutation Network
IEEE Transactions on Computers
Switch fabric design for high performance IP routers: a survey
Journal of Systems Architecture: the EUROMICRO Journal
Fault tolerance design for large-scale optical switches
Optical Switching and Networking
F10: a fault-tolerant engineered network
nsdi'13 Proceedings of the 10th USENIX conference on Networked Systems Design and Implementation
Journal of Electrical and Computer Engineering
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In their 1982 paper, Adams and Siegel proposed an Extra Stage Cube Interconnection Network that tolerates one switch failure with one extra stage. We extend their results and discover a class of Extra Stage Interconnection Networks that tolerate multiple switch failures with a minimal number of extra stages. Adopting the same fault model as Adams and Siegel, the faulty switches can be bypassed by a pair of demultiplexer/multiplexer combinations. It is easy to show that, to maintain point to point and broadcast connectivities, there must be at least $f$ extra stages to tolerate $f$ switch failures. We present the first known construction of an Extra Stage Interconnection Network that meets this lower-bound. This $n$-dimensional Multistage Interconnection Network has $n+f$ stages and tolerates $f$ switch failures. An n-bit label called mask is used for each stage that indicates the bit differences between the two inputs coming into a common switch. We designed the fault-tolerant construction such that it repeatedly uses the singleton basis of the $n$-dimensional vector space as the stage mask vectors. This construction is further generalized and we prove that an $n$-dimensional Multistage Interconnection Network is optimally fault-tolerant if and only if the mask vectors of every n consecutive stages span the $n$-dimensional vector space.