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- W4386157806 abstract "We focus on maximizing a non-negative k-submodular function under a knapsack constraint. As a generalization of submodular functions, a k-submodular function considers k distinct, non-overlapping subsets instead of a single subset as input. We explore the algorithm of Greedy+Singleton, which returns the better one between the best singleton solution and the fully greedy solution. When the function is monotone, we prove that Greedy+Singleton achieves an approximation ratio of $$frac{1}{4}(1-frac{1}{e^2})approx 0.216$$ , improving the previous analysis of 0.158 in the literature. Further, we provide the first analysis of Greedy+Singleton for non-monotone functions, and prove an approximation ratio of $$frac{1}{6}(1-frac{1}{e^3})approx 0.158$$ ." @default.
- W4386157806 created "2023-08-26" @default.
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- W4386157806 date "2023-01-01" @default.
- W4386157806 modified "2023-09-25" @default.
- W4386157806 title "An Improved Analysis of the Greedy+Singleton Algorithm for k-Submodular Knapsack Maximization" @default.
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- W4386157806 doi "https://doi.org/10.1007/978-3-031-39344-0_2" @default.
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