Under Gap-ETH, the n^{O(1/ε^{d-1})}-time shifting PTAS is optimal for maximum independent set, minimum dominating set, maximum induced forest, maximum induced matching, and minimum piercing set on unit ball graphs in every constant dimension d≥2.
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Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes
Under Gap-ETH, the n^{O(1/ε^{d-1})}-time shifting PTAS is optimal for maximum independent set, minimum dominating set, maximum induced forest, maximum induced matching, and minimum piercing set on unit ball graphs in every constant dimension d≥2.