Extra Local Diagnosability of Networks under the MM* Model

故障诊断对提升大规模网络可靠性意义重大。实际应用中，往往无需全局诊断，仅需确定信息传输区域内特定顶点(处理器)的工作状态。为此提出局部诊断方法，即设计包含特定顶点v的子网络，通过分析该子网络基于诊断模型得到的症状判断v是否故障。为保障故障网络局部连通性，引入h-限制故障模型，该模型要求移除所有故障顶点后网络的每个连通分量所含顶点数大于h。基于此，进一步提出h-限制局部可诊断性的概念，并给出在MM*模型下估计顶点v的限制局部可诊断性的充分条件，同时设计了包含顶点v的子网络结构 TM( v;h ) 。Fault diagnosis is crucial for improving the reliability of large-scale networks. In practice, it is often unnecessary to diagnose the entire network. Instead, determining the operational status of specific vertices (processors) within a particular information transmission region is more important. To address this, we propose a local diagnosis method that constructs a sub-network containing a specific vertex v. By analyzing the symptoms of this sub-network under a given diagnosis model, we can determine whether v is faulty. To ensure local network connectivity in the presence of faults, we introduce the h-extra fault model. This model requires that after removing all faulty vertices, each connected component of the network must have more than h vertices. Based on this, we further introduce the concept of h-extra local diagnosability. We provide sufficient conditions for estimating the extra local diagnosability of a vertex v under the MM* model and design a sub-network structure TM( v;h ) that includes vertex v.