Bus interconnection networks

AbstractIn bus interconnection networks every bus provides a communication medium between a set of processors. These networks are modeled by hypergraphs where vertices represent the processors and edges represent the buses. We survey the results obtained on the construction methods that connect a large number of processors in a bus network with given maximum processor degree Δ, maximum bus size r, and network diameter D. (In hypergraph terminology this problem is known as the (Δ,D, r)-hypergraph problem.)The problem for point-to-point networks (the case r = 2) has been extensively studied in the literature. As a result, several families of networks have been proposed. Some of these point-to-point networks can be used in the construction of bus networks. One approach is to consider the dual of the network. We survey some families of bus networks obtained in this manner. Another approach is to view the point-to-point networks as a special case of the bus networks and to generalize the known constructions to bus networks. We provide a summary of the tools developed in the theory of hypergraphs and directed hypergraphs to handle this approach

Line Directed Hypergraphs

In this article we generalize the concept of line digraphs to line dihypergraphs. We give some general properties in particular concerning connectivity parameters of dihypergraphs and their line dihypergraphs, like the fact that the arc connectivity of a line dihypergraph is greater than or equal to that of the original dihypergraph. Then we show that the De Bruijn and Kautz dihypergraphs (which are among the best known bus networks) are iterated line digraphs. Finally we give short proofs that they are highly connected

Structural properties and labeling of graphs

The complexity in building massive scale parallel processing systems has re- sulted in a growing interest in the study of interconnection networks design. Network design affects the performance, cost, scalability, and availability of parallel computers. Therefore, discovering a good structure of the network is one of the basic issues. From modeling point of view, the structure of networks can be naturally stud- ied in terms of graph theory. Several common desirable features of networks, such as large number of processing elements, good throughput, short data com- munication delay, modularity, good fault tolerance and diameter vulnerability correspond to properties of the underlying graphs of networks, including large number of vertices, small diameter, high connectivity and overall balance (or regularity) of the graph or digraph. The first part of this thesis deals with the issue of interconnection networks ad- dressing system. From graph theory point of view, this issue is mainly related to a graph labeling. We investigate a special family of graph labeling, namely antimagic labeling of a class of disconnected graphs. We present new results in super (a; d)-edge antimagic total labeling for disjoint union of multiple copies of special families of graphs. The second part of this thesis deals with the issue of regularity of digraphs with the number of vertices close to the upper bound, called the Moore bound, which is unobtainable for most values of out-degree and diameter. Regularity of the underlying graph of a network is often considered to be essential since the flow of messages and exchange of data between processing elements will be on average faster if there is a similar number of interconnections coming in and going out of each processing element. This means that the in-degree and out-degree of each processing element must be the same or almost the same. Our new results show that digraphs of order two less than Moore bound are either diregular or almost diregular.Doctor of Philosoph

Topology as a Factor in Overlay Networks Designed to Support Dynamic Systems Modeling

Overlay networks are logical networks embedded in physical substrate networks. They are useful for supporting specialized applications involving computation and information exchange among subsets of users. This paper examines the characteristics of overlays that make them suitable for different applications in dynamic, distributed database environments. One such characteristic is the ease with which distances between nodes can be calculated. Examples of overlay graph structures that exhibit certain desirable characteristics include the hypercube, toroidal grid graph and the Kautz graph. Applications involving mobile elements are examined, and a system designed to support comparative analysis of the performance of different overlay structures is discussed.13th International Conference on Intelligent Networking and Collaborative Systems (INCoS-2021), September 1-3, 2021, Asia University, Virtual Conference (Online Presentation

The edge fault-diameter of Cartesian graph bundles

AbstractA Cartesian graph bundle is a generalization of a graph covering and a Cartesian graph product. Let G be a kG-edge connected graph and D̄c(G) be the largest diameter of subgraphs of G obtained by deleting c<kG edges. We prove that D̄a+b+1(G)≤D̄a(F)+D̄b(B)+1 if G is a graph bundle with fibre F over base B, a<kF, and b<kB. As an auxiliary result we prove that the edge-connectivity of graph bundle G is at least kF+kB

ON VULNERABILITY MEASURES OF NETWORKS

As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication networks are discussed including the connectivities, fault diameters, and measures based on Hosoya-Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved