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研究生:石舜仁
研究生(外文):Shih, Sun-Jen
論文名稱:三環式網路Hyper-L型的研究
論文名稱(外文):The Study of Hyper-L Tiles of Triple-Loop Networks
指導教授:陳秋媛陳秋媛引用關係
指導教授(外文):Chiuyuan Chen
學位類別:碩士
校院名稱:國立交通大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:16
中文關鍵詞:三環式網路
外文關鍵詞:Triple-loop networkHyper-L tilediameter
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在這篇論文中,我們首先簡介由Aguiló, Fiol與Garcia提出的三環式網路Hyper-L型到目前為止的一些研究結果。 接著我們簡介由Aguiló-Gost提出的H1和H2 Hyper-L型。最後,我們提出這篇論文的主要結果:存在三環式網路與Hyper-L型對應的充分必要條件。

In this thesis, we first survey the current results of hyper-L tiles of triple-loop networks, which were proposed by Aguiló, Fiol and Garcia. Then, we survey the current results of hyper-L H1 and H2, which were proposed by Aguiló-Gost. Finally, we propose our main results ─ necessary and sufficient conditions for the existence of hyper-L triple-loop networks.
Abstract (in Chinese) i
Abstract (in English) ii
Acknowledgement iii
Contents iv
List of Figures v
List of Tables vi
1. Introduction 1
2. Previous results of hyper-L tiles 5
3. New dense families proposed by Aguiló-Gost 8
4. Main results -- necessary and
sufficient conditions of hyper-L tiles 11
5. Concluding remarks 15
References 16

F. Aguiló-Gost, New dense families of triple loop networks,
Disc. Math. 197/198 (1999) 15-27.
F. Aguiló, M. A. Fiol and C. Garcia, Triple-loop networks with
small transmission delay, Disc. Math. 167/168 (1997) 3-16.
S. Chen, W. Gu, Exact order of subsets of asymptotic bases, J.
Number Theory. 41 (1992) 15-21.
C. Chen and F. K. Hwang, The minimum distance diagram of
double-loop networks, IEEE Trans. Comput. 49 (2000), 977-979.
C. Chen, F. K. Hwang, J. S. Lee and S. J. Shih, The Existence of Hyper-L Triple-Loop Networks, preprint..
M. A. Fiol, On congruence in Z^n and the diamesion of a multidimensional circulant, Disc. Math. 141 (1995) 123-134.
M. A. Fiol, M. Valero, J. L. A. Yebra, I. Alegre, and T. Lang,
Optimization of double-loop structures for local networks, Proc. XIX Int. Symp. MIMI'82, Paris, France (1982), 37-41.
M. A. Fiol, J. L. A. Yebra, I. Alegre, and M. Valero, A discrete optimization problem in local networks and data alignment, IEEE Trans. Comput. C-36 (1987), 702-713.
D. F. Hsu, X. Jia, Extermal problems in the construction of
distributed loop networks, SIAM J. Discrete Math. 7 (1994) 57-71.
C. K. Wong and D. Coppersmith, A combinatorial problem related to multimodule organizations, J. Assoc. Comput. Mach. 21 (1974)
392-402.

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