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題名 | Fault-Tolerant Q-Ary K-Cube Networks by Adding Extra Dimensions Based on Coding Theory=應用編碼理論加額外維度的容錯多進位多方體 |
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作者 | 蔡智強; 郭斯彥; Tsai, Jichiang; Kuo, Sy-yen; |
期刊 | 國立臺灣大學工程學刊 |
出版日期 | 19980600 |
卷期 | 73 1998.06[民87.06] |
頁次 | 頁21-38 |
分類號 | 312.23 |
語文 | eng |
關鍵詞 | 多進位多方體; 容錯; 額外維度; 編碼理論; 重組結構; Q-ary k-cube networks; Fault tolerance; Extra dimensions; Coding theory; Reconfiguration; |
中文摘要 | 點至點的多進位多方體及其相關網路現今被使用在很多實驗和學術的平行電腦上 。這些網路的連線 / 開關能被分類成組, 每一組稱為一個維度。因此額外維度的連線 / 開 關能以某特定方法被加入至這些網路, 產生較好的容錯能力,以致於當有連線 / 開關錯誤 存在時,剩下的良好部份仍保證包含一個原來結構和大小的無錯誤網路。在這篇論文中,我 們研究加容錯維度至多進位多方體型態網路的構想;藉著應用編碼理論,當進位值是質數時 ,我們發現選擇適當維度的充份必要條件。 我們的結果比前人在 [6,7] 所作的更為廣泛。 一個根據此條件來建造容錯網路的有效方法也被提出;只要相對應的最佳線性碼存在,我們 的方法可達到在網路上加最少數目額外維度的目標。 |
英文摘要 | Point-to-point q-ary k-cube and related networks are being used in many experimental and commercial parallel computers. The links/switches in these networks can be partitioned into groups. Each group is called a dimension. Thus extra dimensions of links/switches can be added to these networks in certain ways resulting in better fault tolerance capabilities, so that even in the presence of link/switch faults, the remaining healthy portion is guaranteed to contain a fault-free network of original structure and size. In this paper, we investigate the idea of adding fault-tolerant dimensions to q-ary k-cube based networks. By exploiting coding theory, we find the necessary and sufficient condition of selecting appropriate extra dimensions when q is a prime. Our result is much more general than the previous works in [6,7]. An efficient approach to constructing fault-tolerant networks based on this condition is also proposed. Our approach achieves the goal by adding minimum number of extra dimensions in a network as long as there exists a corresponding optimal linear code. |
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