| The construction of infinite families of any κ-tight optimal and singular κ-tight optimal directed double loop networks |
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| 基金项目： | This work was supported by the Natural Science Foundation of Fujian Province (Grant No. A0510021) and Science and Technology Three Projects Foundation of Fujian Province (Grant No. 2006F5068) |
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| 摘 要： | The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems. Given the number n of nodes, how to construct a DLN which has minimum diameter? This problem has attracted great attention. A related and longtime unsolved problem is for any given non-negative integer k, is there an infinite family of k-tight optimal DLN? In this paper, two main results are obtained (1) for any k ≥ 0, the infinite families of k-tight optimal DLN can be constructed, where the number n(k,e,c) of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c. (2) for any k ≥ 0,an infinite family of singular k-tight optimal DLN can be constructed.
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| 收稿时间： | 27 May 2006 |
| 修稿时间： | 3 April 2007 |
The construction of infinite families of any <Emphasis Type="Italic">k</Emphasis>-tight optimal and singular <Emphasis Type="Italic">k</Emphasis>-tight optimal directed double loop networks |
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| Authors: | Bao-xing Chen Xie-bin Chen Ji-xiang Meng Wen-jun Xiao |
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| Institution: | (1) Department of Computer Science, Zhangzhou Teachers College, Zhangzhou, 363000, China;(2) Department of Mathematics and Information Science, Zhangzhou Teachers College, Zhangzhou, 363000, China;(3) College of Mathematics & System Science, Xinjiang University, Urumqi, 830046, China;(4) Department of Computer Science, South China University of Technology, Guangzhou, 510641, China |
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| Abstract: | The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems. Given the number n of nodes, how to construct a DLN which has minimum diameter? This problem has attracted great attention. A related and longtime unsolved problem is: for any given non-negative integer k, is there an infinite family of k-tight optimal DLN? In this paper, two main results are obtained: (1) for any k ? 0, the infinite families of k-tight optimal DLN can be constructed, where the number n(k, e, c) of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c. (2) for any k ? 0, an infinite family of singular k-tight optimal DLN can be constructed. |
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| Keywords: | double loop network diameter k-tight optimal singular k-tight optimal |
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