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Both Dally and Agarwal also note the difficulty in mapping higher-dimensional network topologies onto a plane. Higher-dimensional networks necessarily have longer interconnection distance, and hence longer propagation delay between nodes, than low-dimensional networks. This can have a significant difference on network performance and can be especially advantageous to direct low-dimensional networks, In these networks, interconnect locality has an even more dramatic effect than that discussed in the preceding section. (See problem 14.) |
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Wires vs. Computing Elements: links vs. Nodes |
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Historically, the multiprocessor size (and hence its interconnection distance and bandwidth) was determined largely by the physical size of the computing elements or nodes. Under such circumstances, it makes sense to increase the number of links as the network increases; thus, hypercube interconnect technology is preferable to simple meshcoupled processor interconnect topologies. As processors shrink, wires tend to dominate and determine the total interconnection delays and interconnection bandwidth. This is especially true when the wires or links that represent the interconnections between nodes are mapped onto a planar surface for implementation. Thus, as processing elements shrink in size, issues concerning the size and extent of the links determine an optimum network topology. |
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Networks must be implemented in two or three physical dimensions. Even if the interconnections were optical, the same principles would apply as with the wire-based network. Free-space optics, where connections are established via multifaceted holograms, may at least in part alter the wire-based analysis of network optimality [234]. After all, optical signals do not interfere with one another and, in fact, multiple optical signals can be concurrently redirected from a single hologram without losing signal integrity. Unless and until some alternative such as free-space optics is fully developed as a viable interconnect medium, wire will dominate network considerations. Even if free-space optics proves feasible, it will require a number of the same type of considerations that were present in wire-based optics. After all, even free-space optics must be implemented in three dimensions. |
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8.17 Hotspots and Combining |
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Suppose in a large network a certain memory cell is designated for the synchronization of all processor nodes. Since all N processors must synchronize to this node, even a small amount of synchronization traffic l becomes Nl at the node, creating a traffic hotspot and potentially saturating the node. Pfister and Norton [233] were among the first to point out this phenomenon, which they calltree saturation. Traffic simply saturates the weakest link in the network. Suppose N is the total number of processors (nodes), m is the probability of a processor emitting a message in a |
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