Cardinality constrained submodular maximization for random streams

We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein [ASS19] gave a single-pass (1-1/is an element of-epsilon)-approximation algorithm using only linear memory, but their exponential dependence on " makes it impractical even for epsilon = 0:1. We simplify both the algorithm and the analysis, obtaining an exponential improvement in the epsilon-dependence (in particular, O(k/epsilon) memory). Extending these techniques, we also give a simple (1/e-epsilon)-approximation for non-monotone functions in O(k/epsilon) memory. For the monotone case, we also give a corresponding unconditional hardness barrier of 1-1/e + epsilon for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.