Abstract
A k-submodular function is an extension of the submodular function, which has received extensive attention due to its own value. In this paper, we design two random algorithms to improve the approximation ratio for maximizing the monotone k-submodular function with size constraints. With the total size constraint, we get an approximate ratio of \(\frac{nk}{2nk-1}\), under which the total size of the k disjoint subsets is bounded by \(B\in \mathbb {Z_{+}}\). With the individual size constraint, under which the individual size of the k disjoint subsets are bounded by \(B_{1}, B_{2},\ldots , B_{k}\in \mathbb {Z_{+}}\) respectively, satisfying \(B=\sum _{i=1}^kB_{i}\), we get an approximate ratio of \(\frac{nk}{3nk-2}\).
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Acknowledgements
This paper was supported by the Natural Science Foundation of Shandong Province of China (Nos. ZR2020MA029 and ZR2021MA100) and the National Natural Science Foundation of China (No. 12001335).
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Li, Y., Li, M., Zhou, Y., Liu, Q. (2023). Random Approximation Algorithms for Monotone k-Submodular Function Maximization with Size Constraints. In: Li, M., Sun, X., Wu, X. (eds) Frontiers of Algorithmics. IJTCS-FAW 2023. Lecture Notes in Computer Science, vol 13933. Springer, Cham. https://doi.org/10.1007/978-3-031-39344-0_9
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