Non-Adaptive Prophet Inequalities for Minor-Closed Classes of Matroids

TL;DR

This paper investigates non-adaptive prophet inequalities within minor-closed classes of matroids, establishing the existence of constant-competitive mechanisms for various known classes, expanding understanding beyond graphic matroids.

Contribution

It demonstrates that multiple known classes of matroids admit constant-competitive non-adaptive mechanisms, extending previous results limited to graphic matroids.

Findings

Constant-competitive non-adaptive mechanisms exist for several matroid classes.

The results generalize beyond graphic matroids to other minor-closed classes.

This advances the understanding of prophet inequalities in non-adaptive settings.

Abstract

We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight $2$-competitive mechanism for all matroids. However, it is not known what classes of matroids admit non-adaptive mechanisms with constant guarantee. Recently, it was shown that there are constant-competitive non-adaptive mechanisms for graphic matroids. In this work, we show that various known classes of matroids admit constant-competitive non-adaptive mechanisms.