Abstract Hyper graph matching problems have drawn attention recently due to their ability to embed higher order relations between nodes. In this paper, we formulate hyper graph matching problems as constrained MAP inference problems in graphical models. Whereas previous discrete approaches introduce several global correspondence vectors, we introduce only one global correspondence vector, but several local correspondence vectors. This allows us to decompose the problem into a (linear) bipartite matching problem and several belief propagation sub-problems. Bipartite matching can be solved by traditional approaches, while the belief propagation sub-problem is further decomposed as two sub-problems with optimal substructure. Then a newly proposed dynamic programming procedure is used to solve the belief propagation sub-problem. Experiments show that the proposed methods outperform state-of-the-art techniques for hyper graph matching.