TY - GEN
T1 - A Bicriterion Concentration Inequality and Prophet Inequalities for k-Fold Matroid Unions
AU - Alon, Noga
AU - Gravin, Nick
AU - Pollner, Tristan
AU - Rubinstein, Aviad
AU - Wang, Hongao
AU - Weinberg, S. Matthew
AU - Zhang, Qianfan
N1 - Publisher Copyright:
© Noga Alon, Nick Gravin, Tristan Pollner, Aviad Rubinstein, Hongao Wang, S. Matthew Weinberg, and Qianfan Zhang.
PY - 2025/2/11
Y1 - 2025/2/11
N2 - We investigate prophet inequalities with competitive ratios approaching 1, seeking to generalize k-uniform matroids. We first show that large girth does not suffice: for all k, there exists a matroid of girth ≥ k and a prophet inequality instance on that matroid whose optimal competitive ratio is12. Next, we show k-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio (Formula presented) for any k-fold matroid union. Our prophet inequality follows from an online contention resolution scheme. The key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone 1-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields “Chernoff-strength” concentration for a 1-Lipschitz function that is not (approximately) self-bounding.
AB - We investigate prophet inequalities with competitive ratios approaching 1, seeking to generalize k-uniform matroids. We first show that large girth does not suffice: for all k, there exists a matroid of girth ≥ k and a prophet inequality instance on that matroid whose optimal competitive ratio is12. Next, we show k-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio (Formula presented) for any k-fold matroid union. Our prophet inequality follows from an online contention resolution scheme. The key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone 1-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields “Chernoff-strength” concentration for a 1-Lipschitz function that is not (approximately) self-bounding.
KW - Concentration Inequalities
KW - Online Contention Resolution Schemes
KW - Prophet Inequalities
UR - https://www.scopus.com/pages/publications/85218356306
U2 - 10.4230/LIPIcs.ITCS.2025.4
DO - 10.4230/LIPIcs.ITCS.2025.4
M3 - Conference contribution
AN - SCOPUS:85218356306
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 16th Innovations in Theoretical Computer Science Conference, ITCS 2025
A2 - Meka, Raghu
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 16th Innovations in Theoretical Computer Science Conference, ITCS 2025
Y2 - 7 January 2025 through 10 January 2025
ER -