Communication and fault tolerance algorithms on a class of interconnection networks

In this thesis, we focus our attention on four communication problems, namely the single-node and multinode broadcasting, and the single-node and multinode scattering. These are global communication problems, in the sense that all processors participate in the communication as sources or destinations. Furthermore, the multinode broadcasting and scattering problems are symmetric, meaning that the transmission of messages is symmetric with respect to the origin of the information. All communication problems are studied under the store-and-forward, all-port communication model. In the main part of this thesis, we study the generalized hypercube, the multidimensional torus and the star, three interconnection networks that are currently receiving considerable attention. The star interconnection network was introduced in 1986 as an attractive alternative to the binary hypercube in terms of degree, diameter, fault tolerance, and in several other aspects. Since its introduction, several of its properties have been studied and a variety of algorithms have been developed on it. The torus network is becoming increasingly popular as an underlying topology for distributed memory machines. For fixed dimensionality, the torus has bounded degree and as a consequence it is easier to implement using VLSI technology. Finally, some of the generalized hypercube networks have been proven to be more desirable than the binary hypercube for large multiprocessors, if we consider layout and wiring complexity. The method we use to develop communication algorithms on the above networks is the construction of spanning graphs with special properties to direct the flow of information, a technique previously used for these or other networks. The properties of the spanning graphs are highly dependent on the network characteristics, the specific communication problem under consideration and the current communication model. All of the spanning graphs are constructed so that the network resources are fully utilized. In the final main chapter of this thesis, we make an attempt to generalize the technique used on the above three networks, so that it becomes applicable to a wider class of interconnection networks. As a result, a generalized framework is developed on the networks that belong to a subclass of the Cayley graph based networks. Representative networks that belong to this subclass are the ring, the binary hypercube, the star, the bubble sort, the bisectional, the complete, the multidimensional torus, two networks introduces as extensions to the binary hypercube, and the generalized hypercube, to name a few. The benefit of this method is that several networks, which belong to the same class of Cayley graphs, while exhibiting diversity in terms of their characteristics (such as number of nodes, degree, diameter, average diameter, fault tolerance, etc.), are treated uniformly in terms of some communication problems. (Abstract shortened by UMI.)