## 5 Discussion
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\begin{tabular}{c l} \hline \hline  & **Description of Key Points, Advantages, and Concise Performance Evaluation** \\ \hline [PERSON] et al. [27] & deterministic topology recovery in one pass for binary tree networks without packet losses; rapid topology inference after only a few probes in the presence of packet losses; the probability of error is increasing with the loss rates of the links and decreasing with the number of probes per iteration \\ [PERSON] et al. [28] & extends [27] to (full or general) \(m\)-ary undirected trees; accurately distinguishes among all different 2-by-2 components for DAGs; more accurate with less experiments compared to [29]; smaller complexity and less bandwidth consumption than [31] \\ [PERSON] et al. [30] & deterministically recovers the exact DAG logical topology with a single probing experiment and one probe packet traversing each link; contrary to [28; 29], no synchronization among sources is required \\ [PERSON] et al. [31] & algorithms with polynomial time computational complexity in the network size for topology inference under random errors and failure localization under random and adversarial errors; adversarial error localization under NRSC does not require prior knowledge of the topology \\ \hline [PERSON] et al. [33] & sufficient conditions for successfully identifying a single congested link in any logical network; speed (length of training sequence)/complexity (size of NC packets) trade-off \\ [PERSON] et al. [34] & lower bound on probe size for valid end-to-end observations under NC; consistent estimators of link loss rates based on LA approach; LA achieves better accuracy (lower RMSE) than BP for \(n>400\) \\ [PERSON] et al. [35] & extends [34]; LA using _Method of Row Selection_ (LA-RS) has lower complexity but similar RMSE compared to LA using _Method of Normal Equations_ (LA-NE); bandwidth consumption/estimation accuracy trade-off; LA-RS is more accurate than the BP approach; RMSE decreases as the average link success rate increases; a graph with more sources achieves better estimation accuracy; RMSE linearly increases with the number of nodes \\ [PERSON] et al. [38] & proposes a low complexity algorithm to compute MLEs of link loss rates in multiple-source tree networks with multicast and NC capabilities; the algorithm is efficient as the computation at each node is at worst proportional to the tree depth \\ [PERSON] et al. [37] & extends the work in [38]; NC loss tomography is more efficient than traditional methods without NC; minimum cost routing in polynomial time using NC; BP (applies on trees and on general topologies) versus _MINC-like heuristics_ (introduced in [8] only apply on trees) performance depends on number of sources (the more sources the better for both); the larger the loss rates, the slower the convergence of BP algorithm; BP performance increases as \(n\) increases \\ \hline [PERSON] et al. [52] & CS with weighted \(\ell_{1}\) minimization; weights are determined based on the prior congestion probabilities of links; outperforms (unweighted) \(\ell_{1}\) minimization in terms of estimation accuracy, DR, and FPR \\ [PERSON] et al. [53] & greedy iterative estimation algorithm to locate congested links based on prior probabilities; recovered probability is not very accurate; DR is high, whereas FPR not very good; performance increases while congestion ratio decreases \\ [PERSON] et al. [54] & window-based sequential loss tomography scheme for networks with dynamically changing link loss rates; increases the sparsity of link loss rates by subtracting them from steady-state path loss rates; path construction algorithm between two monitors that maximizes identifiability \\ [PERSON] et al. [56] & estimates the GFT of a node state vector and uses CS to estimate packet loss rates in wireless networks with spatially dependent channels; spatial dependence does not imply strong correlation between neighboring nodes’ loss rates; limited applicability \\ [PERSON] et al. [57] & monitors network for anomaly detection and localizes faulty links using CS; scalable \(\mathcal{O}(\log\mathcal{E})\); cost-effective \\ \hline [PERSON] et al. [45] & link delays as exponential random variables; additive Gaussian clock synchronization error; _constrained_\(\ell_{1}-\ell_{2}\) optimization that outperforms the original one [60] in estimation error and detection probability \\ [PERSON] et al. [46] & reflective NT with a single transceiver for identifying bottleneck links; efficient algorithm for constructing reflective (fully-loop and folded) paths; no clock synchronization required synchronization-free delay tomography; differential routing matrix construction by selecting a path as reference; comparable performance to conventional delay schemes \\ [PERSON] et al. [48] & heterogeneous CS-based delay tomography in mobile networks; crowd-sourcing passive RTT measurements; estimates delays at BSs and at servers from the GFT of the vector of the spatial-dependent delays at BSs; the scheme captures the spatial dependence of delays and is robust to the presence of inactive BSs \\ [PERSON] et al. [49] & extends [50] to link delay estimation with dynamic link operations (i.e., insertion and deletion) and provides an algorithm with better theoretical upper bound on running time; topological constraints represented by a line graph model \\ \hline \hline \end{tabular}
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