5 - Fundamental Conditions for Boolean Network Tomography

Summary

Boolean network tomography is another well-studied branch of network tomography, which addresses the inference of binary performance indicators (e.g., normal vs. failed, or uncongested vs. congested) of internal network elements from the corresponding binary performance indicators on measurement paths. Boolean network tomography fundamentally differs from additive network tomography in that it is a Boolean linear system inversion problem in which each measurement path only provides one bit of information and hence deserves a separate discussion. This chapter introduces a series of identifiability measures (e.g., k-identifiability, maximum identifiability index) to quantify the capability of Boolean network tomography in uniquely detecting and localizing failed/congested network elements. As the definitions of these identifiability measures are combinatorial in nature and hard to verify for large networks, the discussion focuses on polynomial-time verifiable conditions and computable bounds, as well as the associated algorithms.