This thesis collects, in a unified framework, two cores, reflecting the dual nature of my research activity. During my Ph.D., I had the chance to explore different branches of knowledge in Computer Science, and this thesis focuses on the two disciplines where my work was more fertile, that are respectively Boolean Network Tomography and Numerical Linear Algebra and High Performance Computing. Despite these two branches are orthogonal to one another in the fields of application of this thesis, they share a common ground as numerical Linear Algebra is often evoked for solving problems in Optimization, Graph Theory and Compressed Sensing, that are in turn exploited in Boolean Network Tomography with the scope of analysing network performance. In addition, both two disciplines share a multi-disciplinar background; the first one, in terms of the combinatorial and probabilistic analysis that is usually required to interpret data acquired through Boolean Network Tomography techniques, the second one for its vast field of application, including Engineering and scientific modelling of complex systems.