Topology Inference with Multivariate Cumulants: The Möbius Inference Algorithm
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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, based on the joint distribution of end-to-end measurements. 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. We provide three variants of MIA. MIA-T precisely recovers the topology from exact cumulants. MIA-E uses hypothesis testing with a novel statistic, allowing for data-driven topology estimation. Finally, MIA-F provides a modification to MIA-T and MIA-E to significantly reduce the typical computational complexity, under an additional mild assumption. We present numerical examples for all three variants of MIA, including a case study based on the IEEE 118 test case.
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