(1−1/e) approximation in adversarial-injection streaming for monotone submodular maximization

Establish whether it is possible to design a streaming algorithm in the adversarial-injection model for monotone submodular maximization under a cardinality constraint that achieves the offline-optimal approximation ratio of 1−1/e.

Background

The adversarial-injection streaming model interleaves a uniformly random-order stream of genuine items with arbitrary adversarially injected items. The paper improves the analysis of a tree-based algorithm but does not reach the optimal 1−1/e factor known offline.

The authors explicitly list this target as an outstanding challenge for this beyond-worst-case model.

References

Two concrete questions were left open for submodular maximization in this model: (i) whether one can reach the offline-optimal constant (1-1/e), and (ii) whether one can reduce memory to poly(k) elements.

— Accelerating Scientific Research with Gemini: Case Studies and Common Techniques  (2602.03837 - Woodruff et al., 3 Feb 2026) in Subsection “Submodular Function Maximization in a Stream”, Section 7.1