概率环境下的分散匹配
Decentralized Matching in a Probabilistic Environment
摘要：
我们考虑一个模型，重复随机匹配的兼容性是概率，实现第一次代理匹配，并持续在未来。这种模式在零工经济、肾脏交换和导师匹配中有应用。我们问一个$decentralized$匹配过程是否可以近似的最佳在线算法。特别是，我们考虑一个分散的$stable$ $matching$过程中，代理匹配的最兼容的合作伙伴谁不喜欢与其他人匹配，和已知的兼容对继续匹配在所有未来的回合。我们证明，上述过程提供了一个0.316近似的最佳在线算法匹配一般图。我们还提供了一个$\frac{1}{7}$ -近似的多对一的二分匹配，一个$\frac{1}{11}$ -近似的能力匹配一般的图形，和一个$\frac{1}{2k}$ -近似的形成团队的$k$代理。我们的研究结果依赖于一个新的耦合参数，分解成功的边缘的最佳在线算法在他们的一轮又一轮的比较与稳定的匹配。
英文摘要：
We consider a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future. Such a model has applications in the gig economy, kidney exchange, and mentorship matching. We ask whether a $decentralized$ matching process can approximate the optimal online algorithm. In particular, we consider a decentralized $stable$ $matching$ process where agents match with the most compatible partner who does not prefer matching with someone else, and known compatible pairs continue matching in all future rounds. We demonstrate that the above process provides a 0.316-approximation to the optimal online algorithm for matching on general graphs. We also provide a $\frac{1}{7}$-approximation for many-to-one bipartite matching, a $\frac{1}{11}$-approximation for capacitated matching on general graphs, and a $\frac{1}{2k}$-approximation for forming teams of up to $k$ agents. Our results rely on a novel coupling argument that decomposes the successful edges of the optimal online algorithm in terms of their round-by-round comparison with stable matching.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
