Poly(k) memory for adversarial-injection streaming submodular maximization

Develop a streaming algorithm for monotone submodular maximization under a cardinality constraint in the adversarial-injection model that stores only poly(k) elements (polynomial in the solution size k), rather than exponentially many in k, while achieving a constant-factor approximation.

Background

The current tree-based algorithm maintains exponentially many states in k to preserve stream-length independence and approximation guarantees. Reducing the memory footprint to polynomial in k without sacrificing robustness to adversarial injections remains unresolved.

This memory question is listed alongside the (1−1/e) target as a central open direction for this model.