Adaptive submodular maximization has been extensively studied in the literature. However, most of existing studies this field focus on pool-based setting, where one is allowed to pick items any order, and there have few for stream-based setting arrive an arbitrary order must immediately decide whether select item or not upon its arrival. In paper, we introduce a new class utility functions, sem...

We consider the problem of maximizing a non-negative monotone submodular function subject to knapsack constraint, which is also known as Budgeted Submodular Maximization (BSM) problem. Sviridenko (Operat Res Lett 32:41–43, 2004) showed that by guessing 3 appropriate elements an optimal solution, and then executing greedy algorithm, one can obtain approximation ratio $$\alpha =1-{1}/{e} \approx ...