Abstract
In this paper, we investigate the problem of maximizing the difference between an approximately submodular function and a non-negative linear function subject to a matroid constraint. This model has widespread applications in real life, such as the team formation problem in labor market and the assortment optimization in sales market. We provide a bicriteria approximation algorithm with bifactor ratio \((\frac{\gamma }{1+\gamma },1)\), where \(\gamma \in (0,1]\) is a parameter to characterize the approximate submodularity. Our result extends Ene’s recent work on maximizing the difference between a monotone submodular function and a linear function. Also, a generalized version of the proposed algorithm is capable to deal with huge volume data set.
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Acknowledgements
This work was supported by the National Key Research and Development Program of China under Grants 2018AAA0101000. Yicheng Xu was supported by Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS202116).
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Wang, Y., Xu, Y., Yang, X. (2021). On Maximizing the Difference Between an Approximately Submodular Function and a Linear Function Subject to a Matroid Constraint. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_7
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