Mesh-Connected Trees: A Bridge Between Grids and Meshes of Trees

The grid and the mesh of trees (or MOT) are among the best-known parallel architectures in the literature. Both of them enjoy eecient VLSI layouts, simplicity of topology, and a large number of parallel algorithms that can eeciently 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 eeciently as the grid, and MOT algorithms as eeciently 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 signiicant amount of computational versatility ooered 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. (b) Figure 1: A seven-node complete binary tree (a), and the two-dimensional mesh-connected trees obtained from it (b), denoted MCT 2 (7).