1 Steiner tree problem | 2 Belief propagation | 2.1 Preliminaries: graphical models and statistical inference | 2.1.1 Bayesian networks | 2.1.2 Markov random fields | 2.1.3 Factor graphs | 2.1.3 Statistical inference | 2.2 Belief propagation | 2.2.1 Sum-product | 2.2.2 Max-product | 2.2.3 Max-sum | 2.2.4 Complexity and correctness | 2.3 Loopy belief propagation | 2.3.1 Complexity and correctness | 3 BP for PCST | 3.1 Graphical model | $$P(\mathbf{d}, \mathbf{p}) | 3.2 Message-passing equations for loop-free graphs | $$m_{i\rightarrow j} (d_j, p_j) | 3.3 Message-passing equations for graphs with cycles | 3.3.1 Implementation details | 3.3.2 Complete algorithm | 4 Additional features | 4.1 Prize-Collecting Steiner forest problem | 4 Workflow with the package