For monotone submodular maximization, containment pruning has a tight 1-1/e factor; for non-monotone objectives, 1/2-ε algorithms exist that exceed known optimization hardness bounds.
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Submodular Ground-Set Pruning: Monotone Tightness and a Non-Monotone Separation
For monotone submodular maximization, containment pruning has a tight 1-1/e factor; for non-monotone objectives, 1/2-ε algorithms exist that exceed known optimization hardness bounds.