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.

Based on the identifiability measures for Boolean network tomography presented in Chapter 5, this chapter addresses the follow-up question of how to design the measurement system to optimize the identifiability measure of interest, with a focus on the placement of monitoring nodes.Depending on the mechanism to collect measurements, the problem is divided into (1) monitor placement, (2) beacon placement, and (3) monitoring-aware service placement, where the first approach requires monitoring nodes at both endpoints of each measurement path, the second approach requires a monitoring node only at one of the endpoints of each measurement path, and the third approach requires each measurement path to be the default routing path between a client and a server. As many of such problems are NP-hard, the focus is put on establishing the hardness of the optimal solution and developing polynomial-time suboptimal algorithms with performance guarantees. The chapter also covers a suite of path construction problems addressing how to construct or select measurement paths to optimize the tradeoff between identifiability and probing cost.