Boolean network tomography is a powerful tool to infer the state (working/failed) of individual nodes from path-level measurements obtained by edge-nodes. We consider the problem of optimizing the capability of identifying network failures through the design of monitoring schemes. Finding an optimal solution is NP-hard and a large body of work has been devoted to heuristic approaches providing lower bounds. Unlike previous works, we provide upper bounds on the maximum number of identifiable nodes, given the number of monitoring paths and different constraints on the network topology, the routing scheme, and the maximum path length. These upper bounds represent a fundamental limit on identifiability of failures via Boolean network tomography. Our analysis provides insights on how to design topologies and related monitoring schemes to achieve the maximum identifiability under various network settings. Through analysis and experiments we demonstrate the tightness of the bounds and efficacy of the design insights for engineered as well as real networks.

中文翻译：

---

基于布尔网络层析成像的故障可识别性的基本界限

布尔网络断层扫描是一种功能强大的工具，可以从边缘节点获得的路径级别测量值推断各个节点的状态（工作/失败）。我们考虑通过监控方案的设计来优化识别网络故障的能力的问题。寻找最佳解决方案是NP难题，并且大量工作已致力于提供下界的启发式方法。与以前的工作不同，给定监视路径的数量以及网络拓扑，路由方案和最大路径长度的不同约束，我们为可识别节点的最大数量提供了上限。这些上限代表通过布尔网络层析成像对故障的可识别性的基本限制。我们的分析提供有关如何设计拓扑和相关监视方案以在各种网络设置下实现最大可识别性的见解。通过分析和实验，我们证明了针对工程网络和实际网络的紧密联系和设计见解的有效性。