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This article discusses the quadratization of Markov Logic Networks, which enables efficient approximate MAP computation by means of maximum flows. The procedure relies on a pseudo-Boolean representation of the model, and allows handling models of any order. The employed pseudo-Boolean representation can be used to identify problems that are guaranteed to be solvable in low polynomial-time. Results on common benchmark problems show that the proposed approach finds optimal assignments for most variables in excellent computational time and approximate solutions that match the quality of ILP-based solvers.