Practical Parallel Algorithms for Non-Monotone Submodular Maximization

Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing size of datasets in these domains, there is a pressing need to develop efficient and parallelizable algorithms for submodular maximization. One measure of the parallelizability of a submodular maximization algorithm is its adaptive complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose a low-adaptivity algorithm achieving an (1/8 − ϵ)- approximation with practical Õ(n) query complexity. Moreover, we also propose the first algorithm with both provable approximation ratio and sublinear adaptive complexity for the problem of non-monotone submodular maximization subject to a k-system constraint. As a by-product, we show that our two algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our algorithms is demonstrated by extensive experiments on real-world applications.

Authors

• Shuang Cui School of Computer Science and Technology / Suzhou Institute for Advanced Research, University of Science and Technology of China
• Kai Han
• Jing Tang Hebei University of Technology
• Xueying Li Alibaba Group
• Aakas Zhiyuli Alibaba Group
• Hanxiao Li

Keywords

• Data Mining
• machine learning