Abstract
In this paper, we consider the problem of maximizing the sum of a submodular and a supermodular (BP) function (both are non-negative) under cardinality constraint and p-system constraint respectively, which arises in many real-world applications such as data science, machine learning and artificial intelligence. Greedy algorithm is widely used to design an approximation algorithm. However, in many applications, evaluating the value of the objective function is expensive. In order to avoid a waste of time and money, we propose a Stochastic-Greedy (SG) algorithm, a Stochastic-Standard-Greedy (SSG) algorithm as well as a Random-Greedy (RG) for the monotone BP maximization problems under cardinality constraint, p-system constraint as well as the non-monotone BP maximization problems under cardinality constraint, respectively. The SSG algorithm also works well on the monotone BP maximization problems under cardinality constraint. Numerical experiments for the monotone BP maximization under cardinality constraint is made for comparing the SG algorithm and the SSG algorithm in the previous works. The results show that the guarantee of the SG algorithm is worse than the SSG algorithm, but the SG algorithm is faster than SSG algorithm, especially for the large-scale instances.
Supported by Higher Educational Science and Technology Program of Shandong Province (No. J17KA171) and Natural Science Foundation of China (Grant Nos. 11531014, 11871081, 61433012, U1435215).
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Ji, S., Xu, D., Li, M., Wang, Y., Zhang, D. (2020). Stochastic Greedy Algorithm Is Still Good: Maximizing Submodular + Supermodular Functions. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_49
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