Optimal Online Contention Resolution Schemes via Ex-Ante Prophet Inequalities [article]

Euiwoong Lee, Sahil Singla
2018 arXiv   pre-print
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
more » ... Ss 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. We also introduce and design optimal (1-1/e)-random order CRSs for matroids, which are similar to OCRSs but the arrival is chosen uniformly at random.
arXiv:1806.09251v1 fatcat:q3k3lx6e6fevtlfyqxszuczjnq