New Query Lower Bounds for Submodular Function MInimization

@inproceedings{Graur2020NewQL,
  title={New Query Lower Bounds for Submodular Function MInimization},
  author={A. Graur and Tristan Pollner and Vidhya Ramaswamy and S. Weinberg},
  booktitle={ITCS},
  year={2020}
}
We consider submodular function minimization in the oracle model: given black-box access to a submodular set function $f:2^{[n]}\rightarrow \mathbb{R}$, find an element of $\arg\min_S \{f(S)\}$ using as few queries to $f(\cdot)$ as possible. State-of-the-art algorithms succeed with $\tilde{O}(n^2)$ queries [LeeSW15], yet the best-known lower bound has never been improved beyond $n$ [Harvey08]. We provide a query lower bound of $2n$ for submodular function minimization, a $3n/2-2$ query lower… Expand
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