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. We prove tight upper and lower bounds on
the maximal identifiability of failure nodes for specific classes of network
topologies, such as trees and d-dimensional grids, in both directed and
undirected cases. We prove that directed d-dimensional grids with support n
have maximal identifiability d using 2d(n−1)+2 monitors; and in the
undirected case we show that 2d monitors suffice to get identifiability of
d−1. We then study identifiability under embeddings: we establish relations
between maximal identifiability, embeddability and graph dimension when network
topologies are model as DAGs. Our results suggest the design of networks over
N nodes with maximal identifiability Ω(logN) using O(logN)
monitors and a heuristic to boost maximal identifiability on a given network by
simulating d-dimensional grids. We provide positive evidence of this
heuristic through data extracted by exact computation of maximal
identifiability on examples of small real networks