Before revision:  This leads to the first nearly linear time algorithm for submodular maximization over k-extendible systems and k-systems. Finally, the technique is flexible enough to incorporate the intersection of m additional knapsack constraints, while retaining similar approximation guarantees , which are roughly k + 2m + \mathcal{O}(\sqrt{k+m}) for k-systems and  k+2m + \mathcal{O}(\sqrt{m}) for k-extendible systems.
After revision:  Both SimultaneousGreedys and RepeatedGreedy are flexible enough to incorporate the intersection of m additional knapsack constraints, while retaining similar approximation guarantees , which are roughly k + 2m + \mathcal{O}(\sqrt{k+m}) for k-systems and k+2m + \mathcal{O}(\sqrt{m}) for k-extendible systems.