基于多元累积量的拓扑推理：Möbius推理算法
Topology Inference with Multivariate Cumulants: The Möbius Inference Algorithm
摘要：
关于通信网络的监视、管理和设计的许多任务依赖于路由拓扑的知识。然而，拓扑映射的标准方法（即，使用跟踪路由的主动探测）依赖于来自日益不合作的路由器的合作，从而导致信息丢失。网络断层扫描，它使用跨监控路径的附加链路度量（如延迟或日志数据包丢失率）的端到端测量，是一种可能的补救措施。网络断层扫描不需要路由器与traceroute探针合作，并且它已经被用来推断多播树的结构。本文更进一步。我们提供了一个层析成像的方法来推断底层路由拓扑的任意一组监控路径使用的联合分布的端到端的测量，而不作任何假设的路由行为。我们的方法，称为莫比乌斯推理算法（MIA），使用此分布的累积量来量化监测路径之间的高阶相互作用，并应用莫比乌斯反演来“解开”这些相互作用。除了MIA，我们还提供了一个更实用的变体，称为稀疏莫比乌斯推理，它使用各种稀疏矩阵来减少需要估计的累积量的数量和阶数。我们展示了我们的方法的可行性，使用合成的案例研究，基于现实世界的ISP拓扑结构。
英文摘要：
Many tasks regarding the monitoring, management, and design of communication networks rely on knowledge of the routing topology. However, the standard approach to topology mapping--namely, active probing with traceroutes--relies on cooperation from increasingly non-cooperative routers, leading to missing information. Network tomography, which uses end-to-end measurements of additive link metrics (like delays or log packet loss rates) across monitor paths, is a possible remedy. Network tomography does not require that routers cooperate with traceroute probes, and it has already been used to infer the structure of multicast trees. This paper goes a step further. We provide a tomographic method to infer the underlying routing topology of an arbitrary set of monitor paths using the joint distribution of end-to-end measurements, without making any assumptions on routing behavior. Our approach, called the Möbius Inference Algorithm (MIA), uses cumulants of this distribution to quantify high-order interactions among monitor paths, and it applies Möbius inversion to "disentangle" these interactions. In addition to MIA, we provide a more practical variant called Sparse Möbius Inference, which uses various sparsity heuristics to reduce the number and order of cumulants required to be estimated. We show the viability of our approach using synthetic case studies based on real-world ISP topologies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
