  Loss tomography has been studied for more than 10 years and a number of
estimators have been proposed. The estimators can be divided into two classes:
maximum likelihood and non-maximum likelihood. The maximum likelihood
estimators rely on the maximum likelihood principle to ensure the accuracy of
the estimates obtained by the estimators. Unfortunately, all of the maximum
likelihood estimators need to use an iterative procedure to search the solution
space for the maximum or to solve a high degree polynomial. An iterative
procedure can be computationally expensive and may even converge to a local
maximum. On the other hand, the non-maximum likelihood estimators pursue closed
form solutions by scarifying the accuracy of estimates. To overcome the
pitfalls, we, in this paper, propose a closed form and maximum likelihood
estimator to estimate the loss rate of a link in a network. The closed form
solution is built on the discovery of a connection between the number of probes
passing a link and the number of probes passing its parent. The proposed
estimator is applicable to both the tree topology and the general one.
