Free dimensions-an effective approach to achieving fault tolerance in hypercube

In the n-dimensional hypercube, Q/sub n/, for large n, faults can occur with relatively high probability. How to use the inherent redundancy present in the hypercube to obtain fault tolerance is discussed, along with computing in faulty hypercubes. The authors study the fault tolerance independently present in hypercubes by defining and using the concept of free dimensions. Briefly, in Q/sub n/, a dimension is said to be free if no pair of nodes across the dimension link are both faulty. Efficient algorithms are presented for finding free dimensions, given a set of faulty nodes, and it is shown that at least n-f+1 free dimensions exist with f<or=n faulty nodes. Free dimensions can be used to partition Q/sub n/ into subcubes such that each subcube contains at most one fault. Such a partitioning helps in achieving fault tolerance via emulation, embedding, and reconfiguration. It also helps in designing efficient routing and broadcasting algorithms in faulty hypercubes.<<ETX>>

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