Conceptual Graphs Rules were proposed as an extension of Simple Conceptual Graphs (CGs) to represent knowledge of form "if A then B", where A and B are simple CGs. Optimizations of the deduction calculus in this KR formalism include a Backward Chaining that unifies at the same time whole subgraphs of a rule, and a Forward Chaining that relies on compiling dependencies between rules.In this paper, we show that the unification used in the first algorithm is exactly the operation required to compute dependencies in the second one. We also combine the benefits of the two approaches, by using the graph of rules dependencies in a Backward Chaining framework.