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Sequence submodular maximization meets streaming

Author

Listed:
  • Ruiqi Yang

    (Beijing University of Technology
    University of Chinese Academy Sciences)

  • Dachuan Xu

    (Beijing University of Technology)

  • Longkun Guo

    (Qilu University of Technology (Shandong Academy of Sciences))

  • Dongmei Zhang

    (Shandong Jianzhu University)

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 $$(1/(2\varDelta +1)- O(\epsilon ))$$ ( 1 / ( 2 Δ + 1 ) - O ( ϵ ) ) , consumes $$O(k\varDelta /\epsilon )$$ O ( k Δ / ϵ ) memory source in total and $$O(\log (k\varDelta )/\epsilon )$$ O ( log ( k Δ ) / ϵ ) update time per edge, where $$\varDelta $$ Δ is the minimum of the maximal outdegree and indegree of the directed graph.

Suggested Citation

  • Ruiqi Yang & Dachuan Xu & Longkun Guo & Dongmei Zhang, 2021. "Sequence submodular maximization meets streaming," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 43-55, January.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:1:d:10.1007_s10878-020-00662-5
    DOI: 10.1007/s10878-020-00662-5
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Zengfu Wang & Bill Moran & Xuezhi Wang & Quan Pan, 2016. "Approximation for maximizing monotone non-decreasing set functions with a greedy method," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 29-43, January.
    3. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Yijing Wang & Dachuan Xu & Yishui Wang & Dongmei Zhang, 2020. "Non-submodular maximization on massive data streams," Journal of Global Optimization, Springer, vol. 76(4), pages 729-743, April.
    5. Ruiqi Yang & Dachuan Xu & Yanjun Jiang & Yishui Wang & Dongmei Zhang, 2019. "Approximating Robust Parameterized Submodular Function Maximization in Large-Scales," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-24, August.
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