Abstract
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. The bounds take into consideration two different classes of routing schemes (arbitrary and consistent routing) as well as quality of service (QoS) requirements. We formally prove the tightness of such bounds for the arbitrary routing scheme, and provide an algorithmic approach to the design of network topologies and path deployment that meet the discussed limits. Due to the computational complexity of the optimal solution, We evaluate the tightness of our lower bounds by comparing their values with an upper bound, obtained by a state-of-the-art heuristic for node identifiability. For our experiments we run extensive simulations on both synthetic and real network topologies, for which we show that the two bounds are close to each other, despite the fact that the provided lower bounds are topology agnostic.
Highlights
With the massive growth of the Internet, localizing node failures has become a crucial task
We study how the routing scheme affects the bound values by giving two different formulations, for arbitrary and consistent routing, respectively
We study how requirements on the maximum and average path length affect the bound formulation, highlighting the dependence of the minimal number of required paths on quality of service (QoS) constraints
Summary
With the massive growth of the Internet, localizing node failures has become a crucial task. Observations of the outcome of monitoring paths (working/failed) induce a system of Boolean equations where the unknowns are the Boolean states of the nodes in the network. We provide topology-agnostic lower-bounds to the minimum number of measurement paths which are necessary to guarantee identifiability to a desired number of nodes. Such bounds represent the dual solution to the optimization problem studied in [4], where we introduced upper-bounds to the maximum number of identifiable nodes given a number of monitoring paths. We study theoretical bounds on the minimum number of paths to deploy in a network for identifying a desired number of nodes. For this purpose we compare the bounds with the results of a state-of-the-art greedy algorithm, hereby referred to as Greedy for Identifiability (GI), for maximizing network identifiability by means of client-to-server probing paths [5]
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