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In this paper, we investigate the maximization of the differences between a nonnegative monotone diminishing return submodular (DR-submodular) function and a nonnegative linear function on the integer lattice. As it is almost unapproximable for maximizing a submodular function without the condition of nonnegative, we provide weak (bifactor) approximation algorithms for this problem in two online settings, respectively. For the unconstrained online model, we combine the ideas of single-threshold greedy, binary search and function scaling to give an efficient algorithm with a 1/2 weak approximation ratio. For the online streaming model subject to a cardinality constraint, we provide a one-pass (3-5)/2 weak approximation ratio streaming algorithm. Its memory complexity is (klogk/Ε), and the update time for per element is (log2k/Ε). © Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2022.
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Journal of the Operations Research Society of China
ISSN: 2194-668X
Year: 2024
Issue: 3
Volume: 12
Page: 795-807
Cited Count:
SCOPUS Cited Count: 1
ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 0
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