## 6 Conclusions  
In this review, we presented some of the latest algebraic-based approaches for network tomography, which are expected to have considerable practical and theoretical merit in future communication network infrastructures. We focused on approaches adopting network coding and compressed sensing as their fundamental machinery for inferring various parameters of the network, such as delay and packet loss, or the topology of the network itself. We presented various aspects of some of the specific solutions that have been proposed already. Eventually, we provided a qualitative comparative discussion on the presented techniques, summarizing in tabular form the key features of the selected methods. The outcomes of this comparison can be used as basis for the selection of the most appropriate approach given specific application requirements. From such an analysis, the network coding based approaches seem to be the more appropriate in an idealized setting where network routers can be modified at bulk to execute network coding protocols, while compressed sensing emerged as the more pragmatic and efficient solution that could be realistically applied directly in today's infrastructure, paving the way for more advanced network monitoring solutions.  
All authors have contributed in the conceptualization of the paper. [PERSON] and D.G. have outlined the structure of the paper and have performed extensive literature review. [PERSON] and S.P. have guided the development of the content. All authors have participated in the writing of the manuscript. [PERSON] and D.G. have performed the qualitative comparison and classification of approaches. [PERSON] and S.P. have participated in the classification of approaches and the overall consistency check. All authors have read and agree to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} NT & Network Tomography \\ QoS & Quality of Service \\ ICMP & Internet Control Message Protocol \\ EM & Expectation-Maximization \\ MCMC & Markov Chain Monte Carlo \\ MoM & Method of Moments \\ NC & Network Coding \\ CS & Compressed Sensing \\ OD & Origin-Destination \\ RLNC & Random Linear Network Coding \\ \end{tabular}  
\begin{table}
\begin{tabular}{r l l l l} \hline \hline  & \multicolumn{2}{c}{**Error**} & \multicolumn{1}{c}{**Entropy**} & \multicolumn{1}{c}{**FPR**} & \multicolumn{1}{c}{**DR**} \\  & \multicolumn{1}{c}{**(RMSE)**} & \multicolumn{1}{c}{**Entropy**} & \multicolumn{1}{c}{**FPR**} & \multicolumn{1}{c}{**DR**} \\ \hline _LA-NE_[34] & [0.5\%, 14.0\%) & & & & \\ _LA-RS_[35] & [0.5\%, 15.0\%) & & & & \\ _BP_[37] & [2.0\%, 15.0\%) & & & & \\ _MNC-like heuristic_[37] & & & & & \\  & & & & (\(-350.0\),\(-180.0\)) \({}^{*}\) & & \\  & & & & (\(-360.0\),\(-200.0\)) \({}^{\dagger}\) & & \\ \[PERSON] et al. [52] & (20.0\%, 30.0\%) \({}^{**}\) & & (2.0\%, 8.0\%) & (75.0\%, 100.0\%) \\ [PERSON] et al. [53] & & & & (10.0\%, 30.0\%) & (70.0\%, 100.0\%) \\ [PERSON] et al. [54] & & & & (99.5\%, 100.0\%) \\ [PERSON] et al. [57] & & & & [0.1 0\%] & [99.0\%, 100.0\%] \\ \hline [PERSON] et al. [45] & [2.4\%, 3.5\%] \({}^{\ddagger}\) & & [0\%, 12.0\%) & [40.0\%, 89.0\%) \\ [PERSON] et al. [46] & & & & [18.0\%, 100.0\%] \\ [PERSON] et al. [48] & \(<\)20.0\% & & & \\ \hline \hline \end{tabular} \({}^{*}\) Computed for topology with two sources. \({}^{\dagger}\) Computed for topology with five sources. \({}^{\ddagger}\) Refers to \(\ell_{2}\) norm of estimation error. \({}^{**}\) Refers to normalized \(\ell_{1}\) norm of estimation error.  
\end{table}
Table 3: Quantitative performance evaluation of selected tomographic methods.