A Markov Random Field Approach to Multicast-Based Network Inference Problems

In this paper, we provide a new unified approach to analyze and solve multicast-based network inference problems. We show that the outcome variables induced by the transmission of a multicast packet form a Markov random field on the multicast tree. We present an algorithm that recovers the multicast tree topology based on the values of an additive tree metric on pairs of the terminal nodes. We prove the correctness of the algorithm. We also give several examples of an additive tree metric for which the values on pairs of the terminal nodes can be estimated from traffic measurements taken at the receivers. In addition, we propose an algorithm to recover the link performance parameters from the joint distribution of the outcome variables at the terminal nodes