As the number of servers in a data center network (DCN) increases, the probability of server failures is significantly increased. Traditional connectivity is an important metric to measure the reliability of DCN. However, the traditional connectivity of a DCN based on the condition of arbitrary faulty servers is generally lower. Therefore, it is important to increase the connectivity of a DCN by adding some limited conditions for the faulty server set. As a result, |$g$|-restricted connectivity and |$h$|-extra connectivity, which are two crucial subjects for a DCN’s ability to tolerate faulty servers, were proposed in the literature. In this paper, we study the |$g$|-restricted connectivity and |$h$|-extra connectivity of a new server-centric DCN, called BCDC, based on crossed cube with excellent performance. We prove that the |$g$|-restricted connectivity of BCDC is 4 for |$n=3$| and |$2n+g(n-2)-2$| for |$n\geq 4$|⁠, where |$0\leq g\leq n-3$|⁠, and the |$h$|-extra connectivity of BCDC is 4 for |$n=3$| and |$2n+h(n-2)-2$| for |$n\geq 4$|⁠, where |$0\leq h\leq n-3$|⁠.

中文翻译：

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数据中心网络BCDC的条件可靠性评估

随着数据中心网络（DCN）中服务器数量的增加，服务器故障的可能性将大大增加。传统连接是衡量DCN可靠性的重要指标。但是，基于任意故障服务器情况的DCN的传统连通性通常较低。因此，重要的是通过为故障服务器集添加一些受限条件来增加DCN的连接性。结果，| $ g $ | 限制的连接和| $ h $ | 文献中提出了额外连接，这是DCN容忍故障服务器能力的两个关键主题。在本文中，我们研究| $ g $ | 限制的连接和| $ h $ |基于交叉立方体的新服务器中心DCN（称为BCDC）的额外连接，具有出色的性能。我们证明| $ g $ | - $ n = 3 $ |的BCDC的受限连接为4 和| $ 2n + g（n-2）-2 $ | 为| $ n \ geq 4 $ |⁠，其中| $ 0 \ leq g \ leq n-3 $ |⁠以及| $ h $ | | $ n = 3 $ |的BCDC的超连通性为4 和| $ 2n + h（n-2）-2 $ | 对于| $ N \ GEQ 4 $ |⁠，其中| $ 0 \当量ħ\当量的n-3 $ |⁠。