The 3-ary n-cube, denoted as $Q_n^3$, is an important interconnection network topology proposed for parallel computers, owing to its many desirable properties such as regular and symmetrical structure, and strong scalability, among others. In this paper, we first obtain an exact formula for the minimum wirelength to embed $Q_n^3$ into grids. We then propose a load balancing algorithm for embedding $Q_n^3$ into a square grid with minimum dilation and congestion. Finally, we derive an O(N²) algorithm for embedding $Q_n^3$ into a gird with balanced communication, where N is the number of nodes in $Q_n^3$. Simulation experiments are performed to verify the total wirelength and evaluate the network cost of our proposed embedding algorithm.

As users increasingly befriend others and interact online via their social media accounts, online social networks (OSNs) are expanding rapidly. Confronted with the big data generated by users, it is imperative that data storage be distributed, scalable, and cost-efficient. Yet one of the most significant challenges about this topic is determining how to minimize the cost without deteriorating system performance. Although many storage systems use the distributed key value store, it cannot be directly applied to OSN storage systems. And because users’ data are highly correlated, hash storage leads to frequent inter-server communications, and the high inter-server traffic costs decrease the OSN storage system’s scalability. Previous studies proposed conducting network partitioning and data replication based on social graphs. However, data replication increases storage costs and impacts traffic costs. Here, we consider how to minimize costs from the perspective of data storage, by combining partitioning and replication. Our cost-efficient data storage approach supports scalable OSN storage systems. The proposed approach co-locates frequently interactive users together by conducting partitioning and replication simultaneously while meeting load-balancing constraints. Extensive experiments are undertaken on two realworld traces, and the results show that our approach achieves lower cost compared with state-of-the-art approaches. Thus we conclude that our approach enables economic and scalable OSN data storage.

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.