In this paper, we provide a streaming algorithm for the problem of maximizing the sum of a supermodular function and a nonnegative monotone diminishing return submodular (MDR-submodular) function with a knapsack constraint on the integer lattice. Inspired by the SIEVE-STREAMING algorithm, we present a two-pass streaming algorithm by using the threshold technique. Then, we improve the two-pass streaming algorithm to one-pass and further reduce its space complexity. The proposed algorithms are proved to have polynomial time and space complexity, and a performance guarantee dependent on the curvature of the supermodular function. Finally, we carry out numerical experiments to verify the performance of the algorithm.
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The first author is supported by Natural Science Foundation of Shandong Province (Nos. ZR2022MA034, ZR2019MA022), and Doctoral research foundation of Weifang University (No. 2017BS02). The second author is supported by Fundamental Research Project of Shenzhen City (No. JCYJ20210324102012033) and National Natural Science Foundation of China (No. 11901158), and Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS202116). The third author is supported by National Natural Science Foundation of China (No. 11871081). The fourth author is supported by National Natural Science Foundation of China (No. 12131003).
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A preliminary version of this paper appeared in 10th International Conference on Computational Data and Social Networks (CSoNet2021), 2021, pp. 68-75.
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Tan, J., Xu, Y., Zhang, D. et al. On streaming algorithms for maximizing a supermodular function plus a MDR-submodular function on the integer lattice. J Comb Optim 45, 55 (2023). https://doi.org/10.1007/s10878-023-00986-y
- DR-submodular function
- Supermodular function
- Knapsack constraint
- Threshold greedy algorithm
- Integer lattice