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, We now refine Algo. 2, that performs approximated inference, in order to lower the exponential factor of |V | from |î ??| + 2 to max(|î|, |?|) + 2. The improvement can thus be significant. Theorem 2. Given B 0 = P 0 , one can compute B 1, B T in time O(T · |I| · (|I| + |V |) · ? · |V | +1 )