## AbstractIt is probably fair to say that exact inference in graphical models is considered a solved problem, at least regarding its computational complexity: it is exponential in the treewidth of the graph, and the general solution is given by the Junction-Tree Algorithm. Most recent work on inference has therefore been devoted to the development of approximate algorithms for cases where exact inference is intractable. In this paper, we revisit the exact inference problem and reveal new results. We show that the expected computational complexity of the Junction-Tree Algorithm for MAP inference in graphical models can be improved. Our results apply whenever the potentials over maximal cliques of the triangulated graph are factored over subcliques. The new algorithms are easily implemented, and our experiments reveal substantial speed-ups over the Junction-Tree Algorithm.
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