Congested link inference algorithms only infer the set of share links based on methods of smallest set coverage. When some congested path contains more than one congested link, the inference performance is obviously descending. Aiming at this problem, a version of Lagrange relaxation sub-gradient algorithm based on Bayesian maximum a-posterior (LRSBMAP) is proposed. Aiming at the impacts of congested link inference performance in the different link coverage, and the cost problems of probe deployments and additional E2E active detection, the paper proposes a preliminary selection method for transceiver nodes by optimally selecting degree threshold value (DTV) parameter of IP networks. Through introducing the optimization coefficient ρ, problems of cost and link coverage can be both considered to ensure the performance of inference algorithm. In addition, according to the sparsity of coefficient matrix in link prior probability solution equations, a preconditioned conjugate gradient method based on symmetry successive over-relaxation (PCG_SSOR) is proposed to obtain approximate unique solutions, helping to avoid the solution failures in large scale IP networks under the scenarios of multiple link congestion. Experiments demonstrate that the algorithms proposed in this paper have higher accuracy and robustness.