This chapter covers other canonical applications of network tomography that have been studied in the literature but fallen out of the scope of the previous chapters. This includes the inference of network routing topology (network topology tomography) and the inference of traffic demands (traffic matrix or origin-destination tomography). It also covers miscellaneous techniques used in network tomography that are not covered in the previous chapters (e.g., network coding). The chapter then concludes the book with discussions on practical issues in the deployment of tomography-based monitoring systems and future directions in addressing these issues.

We study compression for function computation of sources at nodes in a network at receiver(s). The rate region of this problem has been considered under restrictive assumptions. We present results that significantly relax these assumptions. For a one-stage tree network, we characterize a rate region by a necessary and sufficient condition for any achievable coloring-based coding scheme, the coloring connectivity condition. We propose a modularized coding scheme based on graph colorings to perform arbitrarily closely to derived rate lower bounds. For a general tree network, we provide a rate lower bound based on graph entropies and show that it is tight for independent sources. We show that, in a general tree network case with independent sources, to achieve the rate lower bound, intermediate nodes should perform computations, but for a family of functions and random variables, which we call chain-rule proper sets, it suffices to have no computations at intermediate nodes to perform arbitrarily closely to the rate lower bound. We consider practicalities of coloring-based coding schemes and propose an efficient algorithm to compute a minimum-entropy coloring of a characteristic graph.