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A short proof for stronger version of DS decomposition in set function optimization

Author

Listed:
  • Xiang Li

    (Santa CLara University)

  • H. George Du

    (University of Texas at Austin)

Abstract

Using a short proof, we show that every set function f can be decomposed into the difference of two monotone increasing and strictly submodular functions g and h, i.e., $$f=g-h$$ f = g - h , and every set function f can also be decomposed into the difference of two monotone increasing and strictly supermodular functions g and h, i.e., $$f=g-h$$ f = g - h .

Suggested Citation

  • Xiang Li & H. George Du, 2020. "A short proof for stronger version of DS decomposition in set function optimization," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 901-906, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00639-4
    DOI: 10.1007/s10878-020-00639-4
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    References listed on IDEAS

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    1. Xiang Li & H. George Du & Panos M. Pardalos, 2020. "A variation of DS decomposition in set function optimization," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 36-44, July.
    2. Ding-Zhu Du & Ker-I Ko & Xiaodong Hu, 2012. "Design and Analysis of Approximation Algorithms," Springer Optimization and Its Applications, Springer, number 978-1-4614-1701-9, June.
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    Cited by:

    1. Qiufen Ni & Hongwei Du, 2021. "On strict submodularity of social influence," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 348-356, February.

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