This paper introduces a new interconnection network suitable for massively parallel architectures. The network has the same node and link complexity as the hypercube and has most of its desirable properties including regularity, recursive structure, partitionability, strong connectivity, and ability to simulate other architectures. In other respects the proposed network has better properties: Its diameter is only about half of the diameter of the hypercube. Mean distance between vertices is smaller and it can simulate a hypercube through dilation 2 embedding. After discussing the basic properties of the proposed network, optimal routing and broadcasting algorithms are developed. The capabilities of the network as an SIMD architecture are demonstrated by giving examples for semigroup computations, matrix multiplication, and sorting. Each of these algorithms requires only about half the number of communication steps compared to their hypercube implementations. Variations of the basic architecture are discussed and it is shown that by introducing simple switches to certain links, a dynamic architecture can be obtained which can be configured into a hypercube topology whenever it is better for a computation. Alternatively, the proposed architecture can be obtained from a hypercube topology by introducing switches to a subset of links. Furthermore, the dynamic reconfiguration capability of the system also improves the embedding properties of the hypercube.

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This paper rst presents some general properties of product networks pertinent to parallel architectures and then focuses on three case studies. These are products of complete binary trees, shu e-exchange, and de Bruijn networks. It is shown that all of these are powerful architectures for parallel computation, as evidenced by their ability to e ciently emulate numerous other architectures. In particular, r-dimensional grids, and r-dimensional meshes of trees can be embedded e ciently in products of these graphs, i.e. either as a subgraph or with small constant dilation and congestion. In addition, the shu e-exchange network can be embedded in r-dimensional product of shu e exchange networks with dilation cost 2r and congestion cost 2. Similarly, the de Bruijn network can be embedded in r-dimensional product of de Bruijn networks with dilation cost r and congestion cost 4. Moreover, it is well known that shu e-exchange and de Bruijn graphs can emulate the hypercube with a small constant slowdown for \normal" algorithms. This means that their product versions can also emulate these hypercube algorithms with constant slowdown. Conclusions include a discussion of many open research areas.

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The grid and the mesh of trees (or MOT) are among the best-known parallel architectures in the literature. Both of them enjoy e cient VLSI layouts, simplicity of topology, and a large number of parallel algorithms that can e ciently execute on them. One drawback of these architectures is that algorithms that perform best on one of them do not perform very well on the other. Thus there is a gap between the algorithmic capabilities of these two architectures.We propose a new class of parallel architectures, called the mesh-connected trees (or MCT) that can execute grid algorithms as e ciently as the grid, and MOT algorithms as e ciently as the MOT, up to a constant amount of slowdown. In particular, the MCT topology contains the MOT as a subgraph and emulates the grid via embedding with dilation 3 and congestion 2. This signi cant amount of computational versatility o ered by the MCT comes at no additional VLSI area cost over these earlier networks. Many topological, routing, and embedding properties analyzed here suggests that the MCT architecture is also a serious competitor for the hypercube. In fact, while the MCT is much simpler and cheaper than the hypercube, for all the algorithms we developed, the running time complexity on the MCT matches those of well-known hypercube algorithms.We also present an interesting variant of the MCT architecture that admits both the MOT and the torus as its subgraphs. While most of the discussion in this paper is focused on the MCT architecture itself, these analyses can be easily extended to the variant of the MCT presented here. K. Efe is with