Streaming algorithms for non-monotone DR-submodular maximization under a knapsack constraint on the integer lattice

Hongyang Zhang () and Wenchang Luo ()
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Hongyang Zhang: Ningbo University
Wenchang Luo: Ningbo University

4OR, 2025, vol. 23, issue 3, No 4, 303-327

Abstract: Abstract Many applications such as Text Summarization, Sensor Placement and Revenue Maximization fall into a general setting: the problem of maximizing a non-monotone DR-submodular function subject to a knapsack constraint on the integer lattice. We consider this problem in the streaming model. By embedding a new binary search into threshold greedy, we propose three streaming algorithms with the corresponding performance guarantees: one-pass $$(\frac{1}{8}-\epsilon )$$ ( 1 8 - ϵ ) -approximation streaming algorithm, two-pass $$(\frac{1}{6}-\epsilon )$$ ( 1 6 - ϵ ) -approximation streaming algorithm, and one-pass $$(\frac{\beta (r-1)}{r-1+3r\beta }-\epsilon )$$ ( β ( r - 1 ) r - 1 + 3 r β - ϵ ) -approximation streaming algorithm. Furthermore, we can also guarantee that our algorithms run in nearly-linear time in the number of nodes and obtain theoretically guaranteed results for Revenue Maximization.

Keywords: Streaming algorithm; Non-monotone DR-submodular maximization; Binary search; Integer lattice; Revenue Maximization; 90C27 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10288-025-00593-z

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