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

A class of communication networks which is suitable for "multiple processor systems" was studied by Pradhan and Reddy. The underlying graph (to be called Shift and Replace graph or SRG) is based on DeBruijn digraphs and is a function of two parameters r and m. Pradhan and Reddy have shown that the node-connectivity of SRG is at least r. The same authors give a routing algorithm which generally requires 2m hops if the number of node failures is ≤(r -1). In this paper we show that the node-connectivity of SRG is (2r - 2). This would immediately imply that the system can tolerate up to (2r - 3) node failures. We then present routing methods for situations with a certain number of node failures. When this number is ≤(r - 2) our routing algorithm requires at most m + 3 + logr m hops if 3 + logr m ≤m. When the number of node failures is ≤(2r - 3) our routing algorithm requires at most m + 5 + logr m hops if 4 + logr m ≤ m. In all the other situations our routing algorithm requires no more than 2m hops. The routing algorithms are shown to be computationally efficient.

Fault-Tolerant Routing in DeBruijn Comrnunication Networks

Roscoe is an operating system implemented at the University of Wisconsin that allows a network of microcomputers to cooperate to provide a general-purpose computing facility. After presenting an overview of the structure of Roscoe, this paper reports on experience with Roscoe and presents several problems currently being investigated by the Roscoe project.

The Roscoe distributed operating system

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.

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Solomon

Papers

Processor Interconnection Strategies