Training processes of structured prediction models such as structural SVMs involve frequent computations of the maximum-a-posteriori (MAP) prediction given a parameterized model. For specific output structures such as sequences or trees, MAP estimates can be computed efficiently by dynamic programming algorithms such as the Viterbi algorithm and the CKY parser. However, when the output structures can be arbitrary graphs, exact calculation of the MAP estimate is an NP-complete problem. In this paper, we compare exact inference and approximate inference for labeling graphs. We study the exact junction tree and the approximate loopy belief propagation and sampling algorithms in terms of performance and ressource requirements.