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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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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.

Cite As Get BibTex

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

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].

Subject Classification

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

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References

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