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arXiv · 2010.04281

Sensitivity Analysis of Submodular Function Maximization

Conor McMeel·Yuichi Yoshida
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Abstract

We study the recently introduced idea of worst-case sensitivity for monotone submodular maximization with cardinality constraint $k$, which captures the degree to which the output argument changes on deletion of an element in the input. We find that for large classes of algorithms that non-trivial sensitivity of $o(k)$ is not possible, even with bounded curvature, and that these results also hold in the distributed framework. However, we also show that in the regime $k = \Omega(n)$ that we can obtain $O(1)$ sensitivity for sufficiently low curvature.

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Conor McMeel, Yuichi Yoshida. 2020-10-08. Sensitivity Analysis of Submodular Function Maximization. https://arxiv.org/abs/2010.04281

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