Streaming Submodular Maximization with the Chance Constraint

Shufang Gong, Bin Liu, Qizhi Fang

Abstract: Submodular optimization plays a significant role in combinatorial problems due to its diminishing marginal return property. Many artificial intelligence and machine learning problems can be cast as submodular maximization problems with applications in object detection, data summarization, and video summarization. In this paper, we consider the problem of monotone submodular function maximization in the streaming setting with the chance constraint. Using mainly the idea of guessing the threshold, we propose streaming algorithms and prove good approximation guarantees and computational complexity. In our experiments, we demonstrate the efficiency of our algorithm on synthetic data for the influence maximization problem and indicate that even if the strong restriction of chance constraint is imposed, we can still get a good solution. To the best of our knowledge, this is the first paper to study the problem of monotone submodular function maximization with chance constraint in the streaming model.