Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path-Based Formulation
成果类型：
Article
署名作者：
Goyal, Vineet; Udwani, Rajan
署名单位：
Columbia University; University of California System; University of California Berkeley
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.2022.2345
发表日期：
2023
页码：
563-580
关键词：
摘要：
The problem of online matching with stochastic rewards is a generalization of the online bipartitematching problemwhere each edge has a probability of success. When a match is made it succeeds with the probability of the corresponding edge. We consider the more general vertex-weighted version of the problem and give two new results. First, we show that a natural generalization of the perturbed-greedy algorithm is (1 - 1/e) competitive when probabilities decompose as a product of two factors, one corresponding to each vertex of the edge. This is the best achievable guarantee as it includes the case of identical probabilities and, in particular, the classical online bipartite matching problem. Second, we give a deterministic 0.596 competitive algorithm for the previously well-studied case of fully heterogeneous but vanishingly small edge probabilities. A key contribution of our approach is the use of novel path-based formulations and a generalization of the primaldual scheme. These allow us to compare against the natural benchmarks of adaptive offline algorithms that knowthe sequence of arrivals and the edge probabilities in advance but not the outcomes of potential matches. These ideas may be of independent interest in other online settingswith postallocation stochasticity.