Showing papers by "Shahram Latifi published in 1991"

Properties and performance of folded hypercubes

Abstract: A new hypercube-type structure, the folded hypercube (FHC), which is basically a standard hypercube with some extra links established between its nodes, is proposed and analyzed. The hardware overhead is almost 1/n, n being the dimensionality of the hypercube, 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 proposed architecture, communication parameters such as average distance, message traffic density, and communication time delay are derived. In addition, some fault tolerance capabilities of this architecture are quantified and compared to those of the standard cube. It is shown that this structure offers substantial improvement over existing hypercube-type networks in terms of the above-mentioned network parameters. >

Subcube embeddability of folded hypercubes

Abstract: The Folded Hypercube (FHC) has been proven to be an attractive hypercube-based network. This paper closely compares the FHC to its standard hypercube counterpart from the subcube allocation viewpoint. It is shown that the FHC(n) outperforms the n-dimensional hypercube (n-cube for short) in offering subcubes of size k by a factor of $\frac{n+1}{n-k+1}$. In an environment where subcubes of the original network must be allocated to incoming tasks, the FHC achieves an excellent processor utilization by assigning subcubes in an efficient and compact manner. Using the concept of virtual hypercubes, an efficient way is suggested to recognize the available subcubes in the FHC by adapting the already developed subcube recognition algorithms. An alternative approach to the subcube recognition problem is also given.