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@inproceedings{zheng2021maximizing,
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@inproceedings{wang2023weakly,
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  author={Wang, Yijing and Zhang, Dongmei and Zhang, Yapu and Zhang, Zhenning},
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  organization={Springer}
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@inproceedings{jiang2023maximizing,
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  year={2023},
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}

@inproceedings{ene2022streaming,
  title={Streaming Algorithm for Monotone k-Submodular Maximization with Cardinality Constraints},
  author={Ene, Alina and Nguyen, Huy},
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  pages={5944--5967},
  year={2022},
  organization={PMLR}
}

@InProceedings{Chen2022Monotone,
author="Chen, Jingwen
and Tang, Zhongzheng
and Wang, Chenhao",
editor="Ni, Qiufen
and Wu, Weili",
title="Monotone k-Submodular Knapsack Maximization: An Analysis of the Greedy+Singleton Algorithm",
booktitle="Algorithmic Aspects in Information and Management",
year="2022",
publisher="Springer International Publishing",
address="Cham",
pages="144--155",
abstract="This paper studies the problem of maximizing a non-negative monotone k-submodular function. A k-submodular function is a generalization of a submodular function, where the input consists of k disjoint subsets, instead of a single subset. For the problem under a knapsack constraint, we consider the algorithm that returns the better solution between the single element of highest value and the result of the fully greedy algorithm, to which we refer as Greedy+Singleton, and prove an approximation ratio {\$}{\$}{\backslash}frac{\{}1{\}}{\{}4{\}}(1-{\backslash}frac{\{}1{\}}{\{}e{\}}){\backslash}approx 0.158{\$}{\$}14(1-1e)≈0.158. Though this ratio is strictly smaller than the best known factor for this problem, Greedy+Singleton is simple, fast, and of special interests. Our experiments demonstrates that the algorithm performs well in terms of the solution quality.",
isbn="978-3-031-16081-3"
}

@inproceedings{chan2021algorithms,
  title={Algorithms for Optimizing the Ratio of Monotone k-Submodular Functions},
  author={Chan, Hau and Loukides, Grigorios and Su, Zhenghui},
  booktitle={Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2020, Ghent, Belgium, September 14--18, 2020, Proceedings, Part III},
  pages={3--19},
  year={2021},
  organization={Springer}
}

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  year={2022}
}

@inproceedings{bei2023bidder,
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@inproceedings{rafiey2020fast,
  title={Fast and Private Submodular and $ k $-Submodular Functions Maximization with Matroid Constraints},
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  pages={7887--7897},
  year={2020},
  organization={PMLR}
}

@article{tang2022monotone,
  title={Monotone k-submodular secretary problems: cardinality and knapsack constraints},
  author={Tang, Zhongzheng and Wang, Chenhao and Chan, Hau},
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  volume={921},
  pages={86--99},
  year={2022},
  publisher={Elsevier}
}



@article{Tang2021OnMaximizing,
title = {On maximizing a monotone k-submodular function under a knapsack constraint},
journal = {Operations Research Letters},
volume = {50},
pages = {28-31},
year = {2022},
author = {Zhongzheng Tang and Chenhao Wang and Hau Chan},
keywords = {-Submodularity, Knapsack, Approximation algorithms},
abstract = {We study the problem of maximizing a non-negative monotone k-submodular function f under a knapsack constraint, where a k-submodular function is a natural generalization of a submodular function to k dimensions. We present a deterministic (12−12e)-approximation algorithm that evaluates f O(n4k3) times, based on the result of Sviridenko (2004) on submodular knapsack maximization.}
}

@inproceedings{ohsaka2015monotone,
 author = {Ohsaka, Naoto and Yoshida, Yuichi},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {C. Cortes and N. Lawrence and D. Lee and M. Sugiyama and R. Garnett},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Monotone k-Submodular Function Maximization with Size Constraints},
 volume = {28},
 year = {2015}
}


