Abstract
In this work, we investigate the problem that maximizes a weakly k-submodular function under the matroid constraint. Different from traditional submodular function maximization, there are k disjoint subsets in k-submodular function optimization, instead of a single set in the submodular maximization. For the weakly k-submodular maximization problem, we provide a greedy algorithm whose approximation ratio is \(\alpha /(1+\alpha )\), where parameter \(0<\alpha \le 1\) is the orthant submodularity ratio. Then we extend to cardinality constraint which maintains the same performance ratio.
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Acknowledgements
The first author is supported by National Natural Science Foundation of China (Nos. 72192804, 72192800) and the Guozhi Xu Posdoctoral Research Foundation. The second author is supported by National Natural Science Foundation of China (No. 11871081). The fourth author is supported by National Natural Science Foundation of China (Nos. 12131003, 12001025).
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Wang, Y., Zhang, D., Zhang, Y., Zhang, Z. (2022). Weakly k-submodular Maximization Under Matroid Constraint. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham. https://doi.org/10.1007/978-3-031-20350-3_32
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DOI: https://doi.org/10.1007/978-3-031-20350-3_32
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