| Summary: | 碩士 === 國立暨南國際大學 === 資訊工程學系 === 93 === The pyramid network (PM, for short) has long been proposed for parallel computing, computer vision, and image processing. The PM is a hierarchy structure base on meshes. In 2004, we proposed a new hierarchy structure, called the enhanced pyramid network (EPM, for short), by replacing each mesh in PM with a torus. Clearly, the EPM is a supergraph of the PM with the same node set. In other words, the PM is a spanning subgraph of the EPM.
In this thesis, we first investigate some topological properties of the EPM. Secondly, we derive a simple algorithm to construct a path between any two distinct nodes in the EPM, and prove that it is a shortest-path routing algorithm. We also proposed an optimal broadcasting algorithm on the EPM with respect to message complexity and transmission delay. And then we calculate the average distance of the EPM. Finally, we show that the EPM is 2-Hamiltonicity. This result is optimal because both the node connectivity and edge connectivity of the EPM are four and at most two faults are tolernable. These results show that the EPM has better topological properties than the PM such as larger node and edge connectivities, smaller average distance, and better fault-tolerant capability. Thus, the EPM is an attractive alternative to the pyramid network.
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