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- W4313350070 abstract "A k-submodular function is a promotion of a submodular function, whose domain is composed of k disjoint subsets rather than a single subset. In this paper, we give a deterministic algorithm for the non-monotone k-submodular function maximization problem subject to a matroid constraint with approximation factor 1/3. Based on this result, we give a randomized 1/3-approximation algorithm for the problem with faster running time, but the probability of success is $$(1-varepsilon )$$ . And we obtain that the complexity of deterministic algorithm and random algorithm is $$O(N|D|(p+kq))$$ and $$O(|D|(plog frac{N}{varepsilon _1}+ k qlog frac{N}{varepsilon _2})log N)$$ respectively, where D is the ground set of the matroid constraint with rank N, p is times of oracle to calculate whether a set is an independent set in this matroid, q is the times of oracle to calculate a value of the k-submodular function, and $$varepsilon , varepsilon _1, varepsilon _2$$ are positive parameters with $$varepsilon =max {varepsilon _1,varepsilon _2}$$ ." @default.
- W4313350070 created "2023-01-06" @default.
- W4313350070 creator A5052024256 @default.
- W4313350070 creator A5054527015 @default.
- W4313350070 creator A5086458292 @default.
- W4313350070 date "2022-01-01" @default.
- W4313350070 modified "2023-09-27" @default.
- W4313350070 title "Maximization of k-Submodular Function with a Matroid Constraint" @default.
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- W4313350070 doi "https://doi.org/10.1007/978-3-031-20350-3_1" @default.
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