“…Monotone nondecreasing submodular functions have been shown with an 1 − 1/e approximation ratio and can be well approximated, i.e., near optimal [17]. Because H D (S, u) is submodular while H D (S, U) is not, we introduce the submodularity ratio and generalized curvature to model H D (S, U) to obtain the guarantees of the greedy framework for regret minimization (or happiness maximization) queries [4], [5], [6], [7], [8], [9]. Lemma 1.…”