In the paper “Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path-Based Formulation,” the authors develop a novel algorithm analysis approach to address stochastic elements in online matching. The approach leads to several new results that were previously out of reach for a fundamental generalization of online matching. More generally, the approach is useful for analyzing the performance of online algorithms for matching in settings with stochastic uncertainty that manifests after matching decisions are made.
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Goyal et al. (2020) studied this question.
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