This book provides the most basic problems, concepts, and well-established results from the topological structure and analysis of interconnection networks in the graph-theoretic language. It covers the basic principles and methods of network design, several well-known networks such as hypercubes, de Bruijn digraphs, Kautz digraphs, double loop, and other networks, and the newest parameters to measure performance of fault-tolerant networks such as Menger number, Rabin number, fault-tolerant diameter, wide-diameter, restricted connectivity, and (l,w)-dominating number. Audience: The book is suitable for those readers who are working on or intend to start research in design analysis of the topological structure of interconnection networks, particularly undergraduates and postgraduates specializing in computer science and applied mathematics.

Topological Structure and Analysis of Interconnection Networks

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Distributed loop computer networks: a survey

Circulant graphs have been extensively investigated over the past 30 years because of their broad application to different fields of theory and practice. Two known surveys on circulant networks including a survey on undirected circulants have been published: by Bermond et al. [Distributed loop computer networks: A survey, J. Parallel Distributed Comput.24 (1995) 2–10] and by Hwang [A survey on multi-loop networks, Theoret. Comput. Sci.299 (2003) 107–121]. The present paper includes the results which have not been presented there, in particular the works of Russian researchers, and also a lot of new results obtained in the area of research of circulant networks. We focus on the survey connected with study of structural and communicative properties of circulant networks.

A survey on undirected circulant graphs

This paper is concerned with a particular family of regular 4-connected graphs, called chordal rings. Chordal rings are a variation of ring networks. By adding two extra links (or chords) at each vertex in a ring network, the reliability and fault-tolerance of the network are enhanced. Two spanning trees on a graph are said to be independent if they are rooted at the same vertex, say, r, and for each vertex v \neq r, the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees on a given graph is said to be independent if they are pairwise independent. Iwasaki et al. [CHECK END OF SENTENCE] proposed a linear time algorithm for finding four independent spanning trees on a chordal ring. In this paper, we give a new linear time algorithm to generate four independent spanning trees with a reduced height in each tree. Moreover, a complete analysis of our improvements on the heights of independent spanning trees is also provided.

Reducing the Height of Independent Spanning Trees in Chordal Rings

This paper deals with a combinatorial problem arising from studies in distributed and parallel architectures. The interconnection network is the heart of parallel computers, and several topologies have been proposed (see [l], [2], [16]). One of the most used is the loop topology, due to its simplicity [13]; in this case, the network consists of a loop (directed or not), which is modeled by a cycle (directed or not). But the simple loop topology has some disadvantages, in particular, its high vulnerability and low performance. Indeed, the network does not work after the failure of one node or arc (in the directed case) or two nodes or edges (in the undirected case). Furthermore, the diameter of the loop network, which corresponds to

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An optimization problem in distributed loop computer networks

The problem under consideration arises from studies on local networks and multimodule memory organizations. The ring network has been one of the popular network topologies used in the design and implementation of local area networks and other configurations. We consider here a generalization of the ring network by adding two fixed-step links to each node. The resulting networks have low diameter, easy routing, and switching structure and therefore are suitable for implementation in the design of reliable networks. Let N denote the number of nodes in the network. For a given N, we are concerned with the problem of determining the best topologies to minimize the diameter (and, hence, the transmission delay) of the network. We obtain new classes of values of N for which topologies can be found that achieve the lower bound lb = [(√2N - 1 - 1)/2] for the minimum diameter. We also show that for some infinite classes of N this lower bound lb is not achievable.

D. F. Hsu

Papers

A combinatorial problem related to distributed loop networks