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Attribute reduction plays an important role in rough set theory. It is an important application in data mining. In this paper, we focus on discussing the relation between set covering and attribute reduction in rough set theory. Based on the equivalence between minimal set covering and minimal attribute reduction sets, attribute reduction graph (ARG) is constructed. A novel algorithm to find the minimal attribute reduction sets, which is based on combination of binary discernibility matrix and graph theory is proposed in this paper. This algorithm demonstrates its efficiency and feasibility by an example.