Work

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

Year: 2026

Type: article

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 ([1]). Previous work showed such concentration results for random variables that come from specific dependent-rounding algorithms ([2, 3]). We discuss some applications of our results to combinatorial optimization and beyond. We also show applications to the concentration of read- k families [4] under certain forms of negative dependence; we further show a simplified proof of the entropy-method approach of [4].

Source: Algorithmica

DOI: 10.1007/s00453-026-01372-w

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

Institutions: University of Maryland, College Park, Carnegie Mellon University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation