A general class of hypercube structures is presented in this paper for interconnecting a network of microcomputers in parallel and distributed environments. The interconnection is based on a mixed radix number system and the technique results in a variety of hypercube structures for a given number of processors N, depending on the desired diameter of the network. A cost optimal realization is obtained through a process of discrete optimization. The performance of such a structure is compared to that of other existing hypercube structures such as Boolean n-cube and nearest neighbor mesh computers.

Generalized Hypercube and Hyperbus Structures for a Computer Network

Generalized hypercube and hyperbus structures for a computer network

A family of regular graphs of degree 3, called Chordal Rings, is presented as a possible candidate for the implementation of a local network of message-connected (micro) computers. For a properly constructed graph in this family having n nodes the diameter, or maximum length message path, is shown to be of 0(n 1/2). The symmetry of the graphs makes it possible to determine message routing by using a simple distributed algorithm. The given algorithm is also potentially useful for the determination of alternate paths in the event of node or link failure.

Analysis of Chordal Ring Network

Analysis of chordal ring network

A family of six-regular graphs, called hexagonal meshes or H-meshes, is considered as a multiprocessor interconnection network. Processing nodes on the periphery of an H-mesh are first wrapped around to achieve regularity and homogeneity. The diameter of a wrapped H-mesh is shown to be of O(p/sup 1/2/), where p is the number of nodes in the H-mesh. An elegant, distributed routing scheme is developed for wrapped H-meshes so that each node in an H-mesh can compute shortest paths from itself to any other node with a straightforward algorithm of O(1) using the addresses of the source-destination pair only, i.e. independent of the network's size. This is in sharp contrast with those previously known algorithms that rely on using routing tables. Furthermore, the authors also develop an efficient point-to-point broadcasting algorithm for the H-meshes which is proved to be optimal in the number of required communication steps. The wrapped H-meshes are compared against some other existing multiprocessor interconnection networks, such as hypercubes, trees, and square meshes. The comparison reinforces the attractiveness of the H-mesh architecture. >

Addressing, routing, and broadcasting in hexagonal mesh multiprocessors

In this paper, we describe four families of topologies for interconnecting many identical processors into a computer network. Each family extends to arbitrarily many processors while keeping the number of neighbors of any one processor fixed. These families are investigated with respect to bus load, routing algorithms, and the relation between the average interprocessor distance and the size of the network.

/pdf/processor-interconnection-strategies-q1u6d1rrvq.pdf

Processor Interconnection Strategies

In this paper we describe a new family of topologies for interconnecting many identical processors to form an MIMD multiprocessor. It extends to arbitrarily many processors while keeping the number of neighbors of any one processor fixed. We show that this family behaves very well with respect to uniformity of bus load, simplicity of routing algorithms, and distance between processors.

/pdf/the-lens-interconnection-strategy-4bpu0v80p8.pdf

Finkel

Papers

Processor Interconnection Strategies

The Lens Interconnection Strategy