## 1.3.4. Switched Multicomputers

1.3.4. Switched Multicomputers

Our last category consists of switched multicomputers. Various interconnection networks have been proposed and built, but all have the property that each CPU has direct and exclusive access to its own, private memory. Figure 1-8 shows two popular topologies, a grid and a hypercube. Grids are easy to understand and lay out on printed circuit boards. They are best suited to problems that have an inherent two-dimensional nature, such as graph theory or vision (e.g., robot eyes or analyzing photographs).

Fig. 1-8. (a) Grid. (b) Hypercube.

A hypercube is an n–dimensional cube. The hypercube of Fig. 1-8(b) is four-dimensional. It can be thought of as two ordinary cubes, each with 8 vertices and 12 edges. Each vertex is a CPU. Each edge is a connection between two CPUs. The corresponding vertices in each of the two cubes are connected.

To expand the hypercube to five dimensions, we would add another set of two interconnected cubes to the figure, connect the corresponding edges in the two halves, and so on. For an n–dimensional hypercube, each CPU has n connections to other CPUs. Thus the complexity of the wiring increases only logarithmically with the size. Since only nearest neighbors are connected, many messages have to make several hops to reach their destination. However, the longest possible path also grows logarithmically with the size, in contrast to the grid, where it grows as the square root of the number of CPUs. Hypercubes with 1024 CPUs have been commercially available for several years, and hypercubes with as many as 16,384 CPUs are starting to become available.

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