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Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint

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Abstract

In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a \((0.363-\varepsilon )\)-approximation algorithm, requiring only a single pass through the data; moreover, we propose a \((0.4-\varepsilon )\)-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and \(\varepsilon \).

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Acknowledgements

The authors thank the referees for their valuable comments on this manuscript.

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Correspondence to Naonori Kakimura.

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A preliminary version appears in The 20th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2017). The second author is partly supported by JSPS KAKENHI Grant Numbers JP17K00028 and JP18H05291. The third author is is partly supported by JST ERATO Grant Number JPMJER1201, and JSPS KAKENHI Grant Number JP17H04676.

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Huang, CC., Kakimura, N. & Yoshida, Y. Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint. Algorithmica 82, 1006–1032 (2020). https://doi.org/10.1007/s00453-019-00628-y

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