Many algorithms for score-based Bayesian net-work structure learning (BNSL), in particularexact ones, take as input a collection of po-tentially optimal parent sets for each variablein the data. Constructing such collectionsnaively is computationally intensive since thenumber of parent sets grows exponentiallywith the number of variables. Thus, pruningtechniques are not only desirable but essen-tial. While good pruning rules exist for theBayesian Information Criterion (BIC), currentresults for the Bayesian Dirichlet equivalentuniform (BDeu) score reduce the search spacevery modestly, hampering the use of the (oftenpreferred) BDeu. We derive new non-trivialtheoretical upper bounds for the BDeu scorethat considerably improve on the state-of-the-art. Since the new bounds are mathematicallyproven to be tighter than previous ones andat little extra computational cost, they are apromising addition to BNSL methods
