Abstract
We consider a two-stage submodular maximization under p-matroid (or p-extendible) constraints. In the model, we are given a collection of submodular functions and some p-matroid (or extendible) system constraints for each of these functions, one need to choose a representative set with a cardinality constraint and simultaneously select a series of subsets that are restricted to the representative set for all functions, the aim is to maximize the average of the summarization of these function values. We extend the two-stage submodular maximization under single matroid to handle p-matroid (or p-extendible) constraints, and derive constant approximation ratio algorithms for the two problems, respectively. In the end, we empirically demonstrate the efficiency of our method on some datasets.
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Acknowledgements
The first and sixth authors are supported by Natural Science Foundation of China (Nos. 11531014, 11871081). The second and fourth authors are supported by Natural Science Foundation (No. 1747818).
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Yang, R., Gu, S., Gao, C., Wu, W., Wang, H., Xu, D. (2019). A Two-Stage Constrained Submodular Maximization. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_30
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DOI: https://doi.org/10.1007/978-3-030-27195-4_30
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