Ricerc@Sapienza

In Boolean Network Tomography (BNT), node identifiability is a crucial property that reflects the possibility of unambiguously classifying the state of the nodes of a network as 'working' or 'failed' through end-to-end measurement paths. Designing a monitoring scheme satisfying network identifiability is an NP problem. In this article, we provide theoretical bounds on the minimum number of necessary measurement paths to guarantee identifiability of a given number of nodes.

We study maximal identifiability, a measure recently introduced in Boolean Network Tomography to characterize networks' capability to localize failure nodes in end-to-end path measurements. Under standard assumptions on topologies and on monitors placement, we prove tight upper and lower bounds on the maximal identifiability of failure nodes for specific classes of network topologies, such as trees, bounded-degree graphs, d-dimensional grids, in both directed and undirected cases.

In this paper we study the node failure identification problem in undirected graphs by means of Boolean Network Tomography. We argue that vertex connectivity plays a central role. We show tight bounds on the maximal identifiability in a particular class of graphs, the Line of Sight networks. We prove slightly weaker bounds on arbitrary networks. Finally we initiate the study of maximal identifiability in random networks. We focus on two models: the classical Erdős-Rényi model, and that of Random Regular graphs.