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

Authors Sharmila Duppala , George Z. Li , Juan Luque, Aravind Srinivasan , Renata Valieva

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ACM Subject Classification
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • Chernoff bounds
  • Submodular Functions
  • Negative Correlation

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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 ([Frederick Qiu and Sahil Singla, 2022]). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms ([Chandra Chekuri et al., 2010; Nicholas J. A. Harvey and Neil Olver, 2014]). We discuss some applications of our results to combinatorial optimization and beyond. We also show applications to the concentration of read-k families [Dmitry Gavinsky et al., 2015] under certain forms of negative dependence; we further show a simplified proof of the entropy-method approach of [Dmitry Gavinsky et al., 2015].

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Sharmila Duppala, George Z. Li, Juan Luque, Aravind Srinivasan, and Renata Valieva. Concentration of Submodular Functions and Read-k Families Under Negative Dependence. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.47

Author Details

Sharmila Duppala
  • University of Maryland, College Park, MD, USA
George Z. Li
  • Carnegie Mellon University, Pittsburgh, PA, USA
Juan Luque
  • University of Maryland, College Park, MD, USA
Aravind Srinivasan
  • University of Maryland, College Park, MD, USA
Renata Valieva
  • University of Maryland, College Park, MD, USA

Funding

All authors are supported in part by NSF award number CCF-1918749.

Acknowledgements

We thank the ITCS 2025 reviewers for their thoughtful comments.

References

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