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The paper continues the study of partitioning based inference of heuristicsfor search in the context of solving the Most Probable Explanation task inBayesian Networks. We compare two systematic Branch and Bound searchalgorithms, BBBT (for which the heuristic information is constructed duringsearch and allows dynamic variable/value ordering) and its predecessor BBMB(for which the heuristic information is pre-compiled), against a number ofpopular local search algorithms for the MPE problem. We show empirically that,when viewed as approximation schemes, BBBT/BBMB are superior to all of thesebest known SLS algorithms, especially when the domain sizes increase beyond 2.This is in contrast with the performance of SLS vs. systematic search onCSP/SAT problems, where SLS often significantly outperforms systematicalgorithms. As far as we know, BBBT/BBMB are currently the best performingalgorithms for solving the MPE task.