Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities

Understand

Online contention resolution schemes (OCRSs) were proposed by Feldman, Svensson, and Zenklusen as a generic technique to round a fractional solution in the matroid polytope in an online fashion.

• It has found applications in several stochastic combinatorial problems where there is a commitment constraint: on seeing the value of a stochastic element, the algorithm has to immediately and irrevocably decide whether to select it while always maintaining an independent set in the matroid.
• Although OCRSs immediately lead to prophet inequalities, these prophet inequalities are not optimal.
• Can we instead use prophet inequalities to design optimal OCRSs? We design the first optimal $1/2$-OCRS for matroids by reducing the problem to designing a matroid prophet inequality where we compare to the stronger benchmark of an ex-ante relaxation.