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Sequence submodular maximization meets streaming

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Abstract

In this paper, we study the problem of maximizing a sequence submodular function in the streaming setting, where the utility function is defined on sequences instead of sets of elements. We encode the sequence submodular maximization with a weighted digraph, in which the weight of a vertex reveals the utility value in selecting a single element and the weight of an edge reveals the additional profit with respect to a certain selection sequence. The edges are visited in a streaming fashion and the aim is to sieve a sequence of at most k elements from the stream, such that the utility is maximized. In this work, we present an edge-based threshold procedure, which makes one pass over the stream, attains an approximation ratio of \((1/(2\varDelta +1)- O(\epsilon ))\), consumes \(O(k\varDelta /\epsilon )\) memory source in total and \(O(\log (k\varDelta )/\epsilon )\) update time per edge, where \(\varDelta \) is the minimum of the maximal outdegree and indegree of the directed graph.

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Acknowledgements

The first two authors are supported by National Natural Science Foundation of China (No. 11531014) and the second author is also supported by Beijing Natural Science Foundation Project No. Z200002. The third author is supported by National Natural Science Foundation of China (No. 61772005) and Natural Science Foundation of Fujian Province (No. 2017J01753). The fourth author is supported by National Natural Science Foundation of China (No. 11871081).

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Authors and Affiliations

  1. Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Ruiqi Yang & Dachuan Xu

  2. School of Mathematical Sciences, University of Chinese Academy Sciences, Beijing, 100049, People’s Republic of China

    Ruiqi Yang

  3. Shandong Key Laboratory of Computer Networks, School of Computer Science and Technology, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, People’s Republic of China

    Longkun Guo

  4. School of Computer Science and Technology, Shandong Jianzhu University, Jinan, 250101, People’s Republic of China

    Dongmei Zhang

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  1. Ruiqi Yang
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  2. Dachuan Xu
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  3. Longkun Guo
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  4. Dongmei Zhang
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Correspondence to Longkun Guo.

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A preliminary version of this paper appeared in Proceedings of the 13th International Conference on Combinatorial Optimization and Applications (COCOA), 2019, pp. 565-575.

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Yang, R., Xu, D., Guo, L. et al. Sequence submodular maximization meets streaming. J Comb Optim 41, 43–55 (2021). https://doi.org/10.1007/s10878-020-00662-5

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