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Network tomography has been widely used recently as an method to infer the network internal link-level characteristics by end-to-end measurement. In this paper, we consider the problem of estimating link loss rates using network tomography. The existing methods make the inference based on the whole tree of network, which is very complex for large scale network. To overcome this limitation, we propose a low complexity inference approach named LCIA. In the LCIA, we deploy monitors at internal nodes to reduce the complexity of inferring the link loss rates. It mainly consists of two steps. The first step is to deploy monitors at specific internal nodes to divide the original tree into several sub-trees with minimum depth. The second step is to infer the link loss rates of sub-trees by a new estimator which is an explicit function of loss measurements. The LCIA has the following features. First, it greatly reduces the inference complexity as the inference on the sub-trees is much simpler. Second, it improves the accuracy of the estimated results since the variance of loss estimator on sub-trees with lower depth is smaller than that on the original tree. The analytical and simulation results demonstrate that the LCIA outperforms the existing methods both on computation complexity and inference accuracy.