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Properties and Performance of Folded Hypercubes
January 1991 (vol. 2 no. 1)
pp. 31-42

A new hypercube-type structure, the folded hypercube (FHC), which is basically astandard hypercube with some extra links established between its nodes, is proposed andanalyzed. The hardware overhead is almost 1/n, n being the dimensionality of thehypercube, which is negligible for large n. For this new design, optimal routing algorithms are developed and proven to be remarkably more efficient than those of the conventional n-cube. For one-to-one communication, each node can reach any other node in the network in at most (n/2) hops (each hop corresponds to the traversal of a single link), as opposed to n hops in the standard hypercube. One-to-all communication (broadcasting) can also be performed in only (n/2) steps, yielding a 50% improvement in broadcasting time over that of the standard hypercube. All routing algorithms are simple and easy to implement. Correctness proofs for the algorithms are given. For the proposedarchitecture, communication parameters such as average distance, message trafficdensity, and communication time delay are derived. In addition, some fault tolerancecapabilities of this architecture are quantified and compared to those of the standardcube. It is shown that this structure offers substantial improvement over existinghypercube-type networks in terms of the above-mentioned network parameters.

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Index Terms:
Index Termsperformance; folded hypercubes; hypercube-type structure; optimal routing algorithms;one-to-one communication; broadcasting; communication parameters; average distance;message traffic density; communication time delay; fault tolerance capabilities; faulttolerant computing; hypercube networks; performance evaluation
A. El-Amawy, S. Latifi, "Properties and Performance of Folded Hypercubes," IEEE Transactions on Parallel and Distributed Systems, vol. 2, no. 1, pp. 31-42, Jan. 1991, doi:10.1109/71.80187
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