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Network tomography has been widely used recently to obtain the network internal characteristics by end-to-end measurement. In this study, the authors consider the problem of estimating link loss rates using network tomography. The existing work based on maximum likelihood estimator (MLE) uses iterative approximation to make the inference, which requires a long execution time for large scale network. To overcome this limitation, the authors propose a fast path-based approach (FPA) by explicit estimation to infer the loss rate of links. Instead of estimating the link loss rates directly, the authors first estimate the path loss rates that are used to derive the link loss rates. In addition, the path loss rates are inferred by a new estimator which is an explicit function of loss observations. The authors evaluate the accuracy of this approach through the analysis of the loss rate estimator and simulation. The estimator is proved to be consistent and have the same asymptotic variance as that of the MLE. The simulation results show that the estimated loss rates using the FPA correctly converge to the real loss rates.