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The paper presents and evaluates the power of a new scheme that generates search heuristics mechanically for problems expressed using a set of functions or relations over a finite set of variables. The heuristics are extracted from a parameterized approximation scheme called Mini-Bucket elimination that allows controlled trade-off between computation and accuracy. The heuristics are used to guide Branch-and-Bound and Best-First search. Their performance is compared on two optimization tasks:doi:10.1016/s0004-3702(01)00107-2 fatcat:qs7bfjxjqbapjas7vpnsa2qs6u