Pairwise-Independent Contention Resolution

TL;DR

This paper develops new online contention resolution schemes and prophet inequalities for non-product distributions, especially pairwise-independent ones, achieving near-optimal ratios for various matroid classes.

Contribution

It introduces OCRSs with high selectability for specific matroids under pairwise-independent distributions, extending the understanding of prophet inequalities in this setting.

Findings

Achieves $(1-o_k(1))$-selectable OCRS for uniform matroids of rank $k$

Provides $ ext{Omega}(1)$-selectable OCRSs for laminar, graphic, cographic, transversal, and regular matroids

Establishes prophet inequalities with similar ratios for pairwise-independent distributions

Abstract

We study online contention resolution schemes (OCRSs) and prophet inequalities for non-product distributions. Specifically, when the active set is sampled according to a pairwise-independent (PI) distribution, we show a $(1-o_k(1))$-selectable OCRS for uniform matroids of rank $k$, and $\Omega(1)$-selectable OCRSs for laminar, graphic, cographic, transversal, and regular matroids. These imply prophet inequalities with the same ratios when the set of values is drawn according to a PI distribution. Our results complement recent work of Dughmi, Kalayci, and Patel (STOC '24) showing that no $\omega(1/k)$-selectable OCRS exists in the PI setting for general matroids of rank $k$.