A Simple and Tight Greedy OCRS
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In recent years, Contention Resolution Schemes (CRSs), introduced by Chekuri, Vondrák, and Zenklusen, have emerged as a general framework for obtaining feasible solutions to combinatorial optimization problems with constraints. The idea is to first solve a continuous relaxation and then round the fractional solution. When one does not have any control on the order of rounding, Online Contention Resolution Schemes (OCRSs) can be used instead, and have been successfully applied in settings such as prophet inequalities and stochastic probing. Intuitively, a greedy OCRS has to decide which elements to include in the integral solution before the online process starts. In this work, we give simple 1/e - selectable greedy OCRSs for rank-1 matroids, partition matroids and transversal matroids. We also show that our greedy OCRSs are optimal, even for the simple single-item case.
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