Embedding of Generalized Fibonacci Cubes in Hypercubes with Faulty Nodes
IEEE Transactions on Parallel and Distributed Systems
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A class of novel interconnection topologies called the generalized Fibonacci cubes is presented. The generalized Fibonacci cubes include the hypercubes, the recently proposed Fibonacci cubes (W.-J. Hsu, Proc. Int. Conf. on Parallel Processing, p.1722-3 (1991)), and some other asymmetric interconnection topologies bridging between the two mentioned above. The generalized Fibonacci cubes can serve as a framework for studying degraded hypercubes due to faulty nodes or links. Previously known algorithms for hypercubes do not generalize to this class of interconnection topologies. The authors present distributed routing and broadcasting algorithms that can be applied to all members of this class of interconnection topologies. It is shown that their distributed routing algorithm always finds a shortest and deadlock-free path. The broadcasting algorithms are designed and evaluated based on both the all-port and the 1-port communication models. The all-port broadcasting algorithm is provably optimal in terms of minimizing routing steps. An upper bound for the 1-port broadcasting algorithm is determined, which is shown to be optimal for certain cases.