For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two...For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two vertices in it.展开更多
The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive propertie...The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ（s, t）. We prove the result in ECQ（s, t）： if s≥3, t≥3, for any two different vertices, all paths whose lengths are between max{9,「s＋1/2」 ＋「t＋1/2＋4}and 2s＋t＋1？1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ（s, t） is「s＋1/2 」＋「t＋1/2 」＋2. The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ（s, t） preserves the path embedding capability to a large extent, while it only has about one half edges of CQn.展开更多
P Kulasinghe and S Bettayeb showed that any multiply-twisted hypercube withfive or more dimensions is not vertex-transitive. This note shows that any multiply-twistedhypercube with four or less dimensions is vertex-tr...P Kulasinghe and S Bettayeb showed that any multiply-twisted hypercube withfive or more dimensions is not vertex-transitive. This note shows that any multiply-twistedhypercube with four or less dimensions is vertex-transitive, and that any multiply-twistedhypercube with three or larger dimensions is not edge-transitive.展开更多
The capability of the data center network largely decides the performance of cloud computing. However, the number of servers in the data center network becomes increasingly huge, because of the continuous growth of th...The capability of the data center network largely decides the performance of cloud computing. However, the number of servers in the data center network becomes increasingly huge, because of the continuous growth of the application requirements. The performance improvement of cloud computing faces great challenges of how to connect a large number of servers in building a data center network with promising performance. Traditional tree-based data center networks have issues of bandwidth bottleneck, failure of single switch, etc. Recently proposed data center networks such as DCell, FiConn, and BCube, have larger bandwidth and better fault-tolerance with respect to traditional tree-based data center networks. Nonetheless, for DCell and FiConn, the fault-tolerant length of path between servers increases in case of failure of switches; BCube requires higher performance in switches when its scale is enlarged. Based on the above considerations, we propose a new server-centric data center network, called BCDC, based on crossed cube with excellent performance. Then, we study the connectivity of BCDC networks. Furthermore, we propose communication algorithms and fault-tolerant routing algorithm of BCDC networks. Moreover, we analyze the performance and time complexities of the proposed algorithms in BCDC networks. Our research will provide the basis for design and implementation of a new family of data center networks.展开更多
文摘For the crossed cube,an equivalent definition based on the quadrilateral is given,by which we obtain the main properties of this topological architecture,and propose a procedure to find a shortest path between any two vertices in it.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos. 61572337 and 61502328, the Program for Postgraduates Research Innovation in University of Jiangsu Province under Grant No. KYLX16_0126, Collaborative Innovation Center of Novel Software Technology and Industrialization, and tile Natural Science Foundation of tile Jiangsu Higher Education Institutions of China under Grant No. 14KJB520034.
文摘The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ（s, t）. We prove the result in ECQ（s, t）： if s≥3, t≥3, for any two different vertices, all paths whose lengths are between max{9,「s＋1/2」 ＋「t＋1/2＋4}and 2s＋t＋1？1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ（s, t） is「s＋1/2 」＋「t＋1/2 」＋2. The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ（s, t） preserves the path embedding capability to a large extent, while it only has about one half edges of CQn.
基金Supported by ANSF(01046102)Supported by the NNSF of China(10271114)
文摘P Kulasinghe and S Bettayeb showed that any multiply-twisted hypercube withfive or more dimensions is not vertex-transitive. This note shows that any multiply-twistedhypercube with four or less dimensions is vertex-transitive, and that any multiply-twistedhypercube with three or larger dimensions is not edge-transitive.
基金This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61572337, 61702351, and 61602333, the Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks Foundation under Grant No. WSNLBKF201701, the China Postdoctoral Science Foundation under Grant No. 172985, the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No. 17KJB520036, the Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No. 1701172B, and the Application Foundation Research of Suzhou of China under Grant No. SYG201653.
文摘The capability of the data center network largely decides the performance of cloud computing. However, the number of servers in the data center network becomes increasingly huge, because of the continuous growth of the application requirements. The performance improvement of cloud computing faces great challenges of how to connect a large number of servers in building a data center network with promising performance. Traditional tree-based data center networks have issues of bandwidth bottleneck, failure of single switch, etc. Recently proposed data center networks such as DCell, FiConn, and BCube, have larger bandwidth and better fault-tolerance with respect to traditional tree-based data center networks. Nonetheless, for DCell and FiConn, the fault-tolerant length of path between servers increases in case of failure of switches; BCube requires higher performance in switches when its scale is enlarged. Based on the above considerations, we propose a new server-centric data center network, called BCDC, based on crossed cube with excellent performance. Then, we study the connectivity of BCDC networks. Furthermore, we propose communication algorithms and fault-tolerant routing algorithm of BCDC networks. Moreover, we analyze the performance and time complexities of the proposed algorithms in BCDC networks. Our research will provide the basis for design and implementation of a new family of data center networks.
