Abstract
In this paper, we consider the problem of maximizing a non-submodular set function subject to a matroid constraint with the continuous generic submodularity ratio \(\gamma \). It quantifies how close a monotone function is to being submodular. As our main contribution, we propose a \((1-e^{-\gamma ^2}-O(\varepsilon ))\)-approximation algorithm when the submodularity ratio is sufficiently large. Our work also can be seen as the first extension of the adaptive sequencing technique in non-submodular case.
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Acknowledgements
The first and second authors are supported by Beijing Natural Science Foundation Project (No. Z200002) and National Natural Science Foundation of China (No. 11871081). The third author is supported by National Natural Science Foundation of China (No. 11871081). The fourth author is supported by Natural Science Foundation of Shandong Province of China (No. ZR2019PA004) and National Natural Science Foundation of China (No. 12001335).
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Sun, X., Xu, D., Zhang, D., Zhou, Y. (2020). An Adaptive Algorithm for Maximization of Non-submodular Function with a Matroid Constraint. In: Chellappan, S., Choo, KK.R., Phan, N. (eds) Computational Data and Social Networks. CSoNet 2020. Lecture Notes in Computer Science(), vol 12575. Springer, Cham. https://doi.org/10.1007/978-3-030-66046-8_1
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