Inference in high-order graphical models has become important in recent years. Several approaches are based, for example, on generalized message-passing, or on transformation to a pairwise model with extra 'auxiliary' variables. We focus on a special case where a much more efficient transformation is possible. Instead of adding variables, we transform the original problem into a comparatively small instance of submodular vertex-cover. These vertex-cover instances can then be attacked by

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... algorithms (e.g. belief propagation, QPBO), where they often run 4-15 times faster and find better solutions than when applied to the original problem. We evaluate our approach on synthetic data, then we show applications within a fast hierarchical clustering and model-fitting framework.