Topology Inference with Multivariate Cumulants: The M\"obius Inference Algorithm

TL;DR

This paper introduces the M"obius Inference Algorithm (MIA), a novel network tomography method that infers routing topology from end-to-end measurements using cumulants and M"obius inversion, without routing assumptions.

Contribution

It presents a new tomographic approach leveraging multivariate cumulants and M"obius inversion to recover network topology from non-cooperative monitor path measurements.

Findings

MIA accurately infers topology in synthetic ISP networks.

Sparse M"obius Inference reduces measurement complexity.

Method works without routing cooperation or assumptions.

Abstract

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 M\"obius Inference Algorithm (MIA), uses cumulants of this distribution to quantify high-order interactions among monitor paths, and it applies M\"obius inversion to "disentangle" these interactions. In addition to MIA, we provide a more practical variant called Sparse M\"obius 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.