Sensitivity Analysis of Submodular Function Maximization
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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 = Ω(n) that we can obtain O(1) sensitivity for sufficiently low curvature.
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