# On Fundamental Bounds of Failure Identifiability by Boolean Network Tomography

## TL;DR

This paper establishes fundamental upper bounds on the number of network nodes whose failures can be identified using Boolean network tomography, guiding optimal network design and monitoring schemes.

## Contribution

It introduces the first theoretical upper bounds on failure identifiability in Boolean network tomography, considering various network constraints and routing schemes.

## Key findings

- Upper bounds are tight and achievable in practice.
- Design insights improve failure detection in real networks.
- Bounds depend on network topology, routing, and path length constraints.

## Abstract

Boolean network tomography is a powerful tool to infer the state (working/failed) of individual nodes from path-level measurements obtained by egde-nodes. We consider the problem of optimizing the capability of identifying network failures through the design of monitoring schemes. Finding an optimal solution is NP-hard and a large body of work has been devoted to heuristic approaches providing lower bounds. Unlike previous works, we provide upper bounds on the maximum number of identifiable nodes, given the number of monitoring paths and different constraints on the network topology, the routing scheme, and the maximum path length. These upper bounds represent a fundamental limit on identifiability of failures via Boolean network tomography. Our analysis provides insights on how to design topologies and related monitoring schemes to achieve the maximum identifiability under various network settings. Through analysis and experiments we demonstrate the tightness of the bounds and efficacy of the design insights for engineered as well as real networks.