Optimal CQ Reformulation is NP-Hard

As a consequence of the Subgoal Theorem and the Projection Lemma, we need only consider projection views that are defined in terms of subgoals. Unfortunately, despite these improvements, we show that the optimization problem is still NP-Hard in the number of subgoals and free variables in the input query. Our proof strategy is as follows. First, we prune the space of potential reformulations by only considering reformulations that preserve the connectivity among the head variables. We call such reformulations as dpp-transforms. Then, we show that computing an optimal dpp-reformulation is NP-Hard by proving that this problem is isomorphic to the Steiner Tree problem [1].