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arXiv · 2309.05554

Concentration of Submodular Functions and Read-k Families Under Negative Dependence

Sharmila Duppala·George Z. Li·Juan Luque·Aravind Srinivasan·Renata Valieva
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Abstract

We study the question of whether submodular functions of random variables satisfying various notions of negative dependence satisfy Chernoff-like concentration inequalities. We prove such a concentration inequality for the lower tail when the random variables satisfy negative association or negative regression, partially resolving an open problem raised in (Qiu and Singla [QS22]). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms (Chekuri, Vondrak, and Zenklusen [CVZ10] and Harvey and Olver [HO14]). We discuss some applications of our results to combinatorial optimization and beyond. We also show applications to the concentration of read-k families [Gav+15] under certain forms of negative dependence; we further show a simplified proof of the entropy-method approach of [Gav+15].

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Sharmila Duppala, George Z. Li, Juan Luque, Aravind Srinivasan, Renata Valieva. 2023-09-11. Concentration of Submodular Functions and Read-k Families Under Negative Dependence. https://arxiv.org/abs/2309.05554

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