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Approximation Algorithms for Non-Submodular Optimization Over Sliding Windows

Author

Listed:
  • Yunxin Luo

    (Institute of Operations Research and Systems Engineering, College of Science, Tianjin, University of Technology, Tianjin 300384, P. R. China)

  • Chenchen Wu

    (Institute of Operations Research and Systems Engineering, College of Science, Tianjin, University of Technology, Tianjin 300384, P. R. China)

  • Chunming Xu

    (Institute of Operations Research and Systems Engineering, College of Science, Tianjin, University of Technology, Tianjin 300384, P. R. China)

Abstract

In this paper, the problem we study is how to maximize a monotone non-submodular function with cardinality constraint. Different from the previous streaming algorithms, this paper mainly considers the sliding window model. Based on the concept of diminishing-return ratio γ, we propose a (1 3γ2 − 𠜀)-approximation algorithm with the memory O(klog2(kΦ 1 γ) 𠜀2), where Φ is the ratio between maximum and minimum values of any singleton element of function f. Then, we improve the approximation ratio to (1 2γ − 𠜀) through the sub-windows at the expense of losing some memory. Our results generalize the corresponding results for the submodular case.

Suggested Citation

  • Yunxin Luo & Chenchen Wu & Chunming Xu, 2022. "Approximation Algorithms for Non-Submodular Optimization Over Sliding Windows," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(05), pages 1-20, October.
    • Handle: RePEc:wsi:apjorx:v:39:y:2022:i:05:n:s021759592150038x
    DOI: 10.1142/S021759592150038X
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