(A) genealization of the debruijn graph for symmetric and fault-tolerant multicomputer interconnection networks

Abstract

A multicomputer system consists of a large number of cooperating computer nodes interconnected in a fixed topology, interconnection network, to increase the computation speed by employing parallelism. The interconnection network should provide adequate performance to avoid becoming a bottleneck of the overall performance. In addition, it should be fault-tolerant since the probability that some nodes in the system will fail increases proportionally to the size of the network. In this thesis, a family of symmetric graphs, called multistage DeBruijn graph, is proposed by generalizing the DeBruijn graph to be used as the interconnection topologies of multicomputer systems. Due to the symmetry, the performance of an interconnection network can be increased by minimizing the congestion problem since the load for message communication will be distributed uniformly through all the nodes and communication links. Moreover, the cost to develop a system can be reduced due to the symmetry since identical hardwares and softwares can be used for each node. It is shown that the proposed graph is a good candidate for symmetric and fault-tolerant interconnection networks by the characteritics of the graph such as the small diameter, vertex-symmetry, edge-symmetry, existence of Hamilton cycles, large fault-tolerance, and existence of wide and short containers. With rgard to performance considerations, the proposed graph is superior to other known symmetric graphs such as the hypercube and the star graph by the fact that the proposed graph contains remarkably larger number of nodes than the others for given degree and diameter. With regard to fault-tolerance considerations, the proposed graph is superior to other known fault-tolerant graphs such as the star graph and the flip-tree by the fact that it has asymptotically best known fault-diameter and container-diameter which are important measures fo fault-tolerance and performance degradation due to faults. Finally, simple and effi...