According to Lin and Bilmes (2011), there exists a simple greedy algorithm for monotonic submodular function maximization where the solution is guaranteed to be close to the real optimum.
if we denote R i greedy as the approximation optimized by greedy algorithm and R i * as the best possible solution, then F( is the objective function of Equation 1 and e ≈ 2.718 denotes the natural constant.