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Maximizing k-submodular functions under budget constraint: applications and streaming algorithms

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Abstract

Motivated by the practical applications in solving plenty of important combinatorial optimization problems, this paper investigates the Budgeted k-Submodular Maximization problem defined as follows: Given a finite set V, a budget B and a k-submodular function \(f: (k+1)^V \mapsto \mathbb {R}_+\), the problem asks to find a solution \(\mathbf{s }=(S_1, S_2, \ldots , S_k) \in (k+1)^V \), in which an element \(e \in V\) has a cost \(c_i(e)\) when added into the i-th set \(S_i\), with the total cost of \(\mathbf{s }\) that does not exceed B so that \(f(\mathbf{s })\) is maximized. To address this problem, we propose two single pass streaming algorithms with approximation guarantees: one for the case that an element e has only one cost value when added to all i-th sets and one for the general case with different values of \(c_i(e)\). We further investigate the performance of our algorithms in two applications of the problem, Influence Maximization with k topics and sensor placement of k types of measures. The experiment results indicate that our algorithms can return competitive results but require fewer the number of queries and running time than the state-of-the-art methods.

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Acknowledgements

This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 102.01-2020.21. The work has been carried out partly at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The first author (Canh V. Pham) would like to thank VIASM for the hospitality and financial support.

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Authors and Affiliations

  1. ORlab, Faculty of Computer Science, Phenikaa University, Hanoi, 12116, Vietnam

    Canh V. Pham

  2. Faculty of Information Security, People’s Security Academy, Hanoi, 10000, Vietnam

    Quang C. Vu

  3. Faculty of Information Technology, University of Engineering and Technology, Vietnam National University, Hanoi, 10000, Vietnam

    Dung K. T. Ha & Tai T. Nguyen

  4. Haiphong University, Haiphong, 180000, Vietnam

    Nguyen D. Le

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  1. Canh V. Pham
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  2. Quang C. Vu
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Correspondence to Canh V. Pham.

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A preliminary version appears in the proceedings of the 10th International Conference on Computational Data and Social Networks. This paper extends and revises the conference version by providing all the proofs more detail and experiment evaluation.

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Pham, C.V., Vu, Q.C., Ha, D.K.T. et al. Maximizing k-submodular functions under budget constraint: applications and streaming algorithms. J Comb Optim 44, 723–751 (2022). https://doi.org/10.1007/s10878-022-00858-x

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