Abstract: When paths share a common congested link, they will all suffer from a performance degradation. Boolean tomography exploits these performance-level correlations between different paths to identify the congested links. It is clear that the congestion of a path will be distinctly intensive when it traverses multiple congested links. We adopt an enlarged state space model to mirror different congestion levels and employ a system of integer equations, instead of Boolean equations, to describe relationships between the path states and the link states. We recast the problem of identifying congested links into a constraint optimization problem, including Boolean tomography as a special case. For a logical tree, we propose an up-to-bottom algorithm and prove that it always achieves a solution to the problem. Compared with existing algorithms, the simulation results show that our proposed algorithm achieves a higher detection rate while keeping a low false positive rate.