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., \(f=g-h\), 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., \(f=g-h\).
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This work is supported in part by NSF CNS-1948550.
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Li, X., Du, H.G. A short proof for stronger version of DS decomposition in set function optimization. J Comb Optim 40, 901–906 (2020). https://doi.org/10.1007/s10878-020-00639-4
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DOI: https://doi.org/10.1007/s10878-020-00639-4