Network coding tomography for network failures

Network Tomography (or network monitoring) uses end-to-end measurements to characterize the network, such as estimating the network topology and localizing random or adversarial glitches. Under the setting that all nodes in the network perform random linear network coding, this work provides a comprehensive study of passive network tomography in the presence of network failures, in particular adversarial/ random errors and adversarial/random erasures. Our results are categorized into two classes: 1. Topology Estimation. In the presence of both adversarial/random failures, we prove it is both necessary and sufficient for all nodes in the network to share common randomness, i.e., the receiver knows the random code-books of other nodes. Without such common randomness, we prove that in the presence of adversarial or random failures it is either theoretically impossible or computationally intractable to estimate topology accurately. With common randomness, we present the first set of algorithms for characterizing topology exactly. Our algorithms for topology estimation in the presence of random errors/erasures have polynomial-time complexity. 2. Failure Localization. Given the topology, we present the first polynomial time algorithms to localize random errors and adversarial erasures. For the problem of locating adversarial errors, we prove that it is intractable.