Submodular maximization problems belong to the family of combinatorial optimization problems and enjoy wide applications. In this paper, we focus on the problem of maximizing a monotone submodular function subject to a @math -knapsack constraint, for which we propose a streaming algorithm that achieves a @math -approximation of the optimal value, while it only needs one single pass through the dataset without storing all the data in the memory. In our experiments, we extensively evaluate the effectiveness of our proposed algorithm via two applications: news recommendation and scientific literature recommendation. It is observed that the proposed streaming algorithm achieves both execution speedup and memory saving by several orders of magnitude, compared with existing approaches.
In this paper, we obtain an (1-e^-^1)-approximation algorithm for maximizing a nondecreasing submodular set function subject to a knapsack constraint. This algorithm requires O(n^5) function value computations.  We treat the text summarization problem as maximizing a submodular function under a budget constraint. We show, both theoretically and empirically, a modified greedy algorithm can efficiently solve the budgeted submodular maximization problem near-optimally, and we derive new approximation bounds in doing so. Experiments on DUC'04 task show that our approach is superior to the best-performing method from the DUC'04 evaluation on ROUGE-1 scores.