Abstract
A k-submodular function is a generalization of a submodular function, whose definition domain is the collection of k disjoint subsets. In our paper, we apply a greedy and local search technique to obtain a \(\frac{1}{6}(1-e^{-2})\)-approximate algorithm for the problem of maximizing a k-submodular function subject to the intersection of a knapsack constraint and a matroid constraint. Furthermore, we use a special analytical method to improve the approximation ratio to \(\frac{1}{3}(1-e^{-3})\), when the k-submodular function is monotone.
Supported by National Science Foundation of China (No. 12001335) and Natural Science Foundation of Shandong Province of China (Nos. ZR2019PA004, ZR2020MA029, ZR2021MA100).
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Yu, K., Li, M., Zhou, Y., Liu, Q. (2022). Guarantees for Maximization of k-Submodular Functions with a Knapsack and a Matroid Constraint. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_14
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