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A Sharp Barrier for Consistent Submodular Maximization: Any Improvement over $2-\sqrt{2}$ Entails Exponential Queries or Linear Recourse

arXiv · AI, language, vision and robotics · article · Sep 9, 2026 · UTC

Consistent submodular maximization studies the tradeoff between solution quality and stability when elements arrive over time. For a monotone submodular objective, which models diminishing returns, an algorithm maintains a set of at most $k$ available elements and changes only $O(1)$ elements after each insertion. Dütting et al. [2025] established a tight $2/3$ approximation with unrestricted computation and a polynomial-time $0.51$ approximation. They left open at STOC 2025 whether efficient algorithms can match the offline $1-1/e$ guarantee. We resolve this problem by proving that the suprem

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