  We aim at assessing the states of the nodes in a network by means of
end-to-end monitoring paths. The contribution of this paper is twofold. First,
we consider a static failure scenario. In this context, we aim at minimizing
the number of probes to obtain failure identification. To face this problem, we
propose a progressive approach to failure localization based on stochastic
optimization, whose solution is the optimal sequence of monitoring paths to
probe.
  We address the complexity of the problem by proposing a greedy strategy in
two variants: one considers exact calculation of posterior probabilities of
node failures, given the observation, whereas the other approximates these
values by means of a novel failure centrality metric. Secondly, we adapt these
two strategies to a dynamic failure scenario where nodes states can change
throughout a monitoring period. By means of numerical experiments conducted on
real network topologies, we demonstrate the practical applicability of our
approach. Our performance evaluation evidences the superiority of our
algorithms with respect to state of the art solutions based on classic Boolean
Network Tomography as well as approaches based on sequential group testing.
