變種超立方體的內崁與通訊

Abstract

本論文針對變種超立方體的內崁與通訊方面作了深入的探討。由於變種超 立方體乃源自於超立方體，不僅保留了超立方體的強連接性、遞迴結構性 和內崁能力，更縮短了約三分之二的直徑而使得訊息的交流比超立方體更 有效率。因此，我們發展了多種傳輸模式的演算法，使得其能在最短時間 內完成訊息的交流。此外，本論文也討論了所發展出來的演算法於平行計 算方面之應用。 The embedding and the communication aspects of the varietal hypercube is investigated in this thesis. The varietal hypercube has most of the desirable properties of the hypercube including strong connectivity, recursive structure, and the flexibility in embedding some commonly used structures. In addition, the diameter of the varietal hypercube is about two third of the hypercube. this implies the communication of the varietal hypercube will be more efficient than that of the hypercube. Algorithms for some common communication modes which guarantee shortest communication time are developed. Several examples of the parallel computing on the varietal hypercube are also provided in this thesis.