在平行計算機器上，嵌入法是一項很重要的應用。在每一項平行的應用中，具有其個別的傳輸架構。這一些傳輸架構，可被映射成為多處理器架構下的拓撲，因此與其相符合的應用將可被執行。本篇論文在具有故障節點的超立方體圖或超立方體衍生圖中，提出一項新的正規圖形階層演算法，包括漢米爾頓路徑(Hamiltonian path)，漢米爾頓迴路(Hamiltonian cycle)，環路(ring)，網格(mesh)，完全二元樹(complete binary tree)，以及費伯納茲立方體(Fibonacci cube)。 首先，在具有故障的節點圖中，找出一個可取代故障節點的點，當n個故障節點出現時，容錯可達擴張度2，延展度3，壅塞度1及負載度1。此外，這種方法也可擴展至超立方體或超立方體衍生圖中。不同於許多目前所見的演算法只能嵌入單一類型的圖，這種演算法以一致的方法嵌入到上述的圖型中。藉由這個結果，我們可以輕鬆的將平行演算法發展到超立方體或超立方體衍生圖的正規圖型架構。此一嵌入的方法非常適合使用於高速的平行電腦中。 Embedding is of great importance in the applications of parallel computing. Every parallel application has its intrinsic communication pattern. The communication pattern graph is mapped into the topology of multiprocessor structures so that the corresponding application can be executed. This thesis proposes a novel algorithm for emulation a class of regular graphs in the faulty hypercube or hypercube derivatives, including the Hamiltonian path, the Hamiltonian cycle, the linear array, the ring, the mesh, the complete binary tree, and the Fibonacci cube. First, to obtain the replaceable node of the faulty node, n faults can be tolerated with expansion 2, dilation 3, congestion 1, and load 1. Furthermore, our method is also extending the distributed fault-tolerant emulation of a class of regular graphs in hypercube or hypercube derivatives. Unlike many existing algorithms which are capable of embedding only type of graphs, our algorithm embeds the above graphs in a unified way. By the results, we can easily port the parallel algorithms developed for the structure of a class of regular graphs to hypercube or hypercube derivatives. This methodology of embedding enables extremely high-speed parallel computation.
