Real-world problems such as ad allocation and matching have been extensively studied under the lens of combinatorial optimization. In several applications, uncertainty in the input appears naturally and this has led to the study of online stochastic optimization models for such problems. For the offline case, these constrained combinatorial optimization problems have been extensively studied, and Contention Resolution Schemes (CRSs), introduced by Chekuri, Vondrák, and Zenklusen, have emerged in recent years as a general framework to obtaining a solution. The idea behind a CRS is to first obtain a fractional solution to a (continuous) relaxation of the objective and then round the fractional solution to an integral one. When the order of rounding is controlled by an adversary, Online Contention Resolution Schemes (OCRSs) can be used instead, and have been successfully applied in settings such as prophet inequalities and stochastic probing. In this work, we focus on greedy OCRSs, which provide guarantees against the strongest possible adversary, an almighty adversary. Intuitively, a greedy OCRS has to make all its decisions before the online process starts.

Matching based markets, like ad auctions, ride-sharing, and eBay, are inherently online and combinatorial, and therefore have been extensively studied under the lens of online stochastic combinatorial optimization models. The general framework that has emerged uses Contention Resolution Schemes (CRSs) introduced by Chekuri, Vondrák, and Zenklusen for combinatorial problems, where one first obtains a fractional solution to a (continuous) relaxation of the objective, and then proceeds to round it. When the order of rounding is controlled by an adversary, it is called an Online Contention Resolution Scheme (OCRSs), which has been successfully applied in online settings such as posted-price mechanisms, prophet inequalities and stochastic probing.The study of greedy OCRSs against an almighty adversary has emerged as one of the most interesting problems since it gives a simple-to-implement scheme against the worst possible scenario. Intuitively, a greedy OCRS has to make all its decisions before the online process starts. This improves upon the previous state-of-the-art greedy OCRSs of [FSZ16] that achieves 1/4 for these constraints.