We present an optimally-competitive algorithm for the problem of maximum online perfect bipartite matching with i.i.d. arrivals. In this problem, we are given a known set of workers, a distribution over job types, and non-negative utility weights for each pair of worker and job types. At each time step, a job is drawn i.i.d. from the distribution over job types. Upon arrival, the job must be irrevocably assigned to a worker and cannot be dropped. The goal is to maximize the expected sum of utilities after all jobs are assigned. We introduce Dispatch, a 0.5-competitive, randomized algorithm. We also prove that 0.5-competitive is the best possible. When a job arrives, Dispatch first selects a “preferred worker” and assigns the job to this worker if it is available. The preferred worker is determined based on an optimal solution to a fractional transportation problem. If the preferred worker is not available, Dispatch randomly selects a worker from the available workers.

中文翻译：

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具有iid到达的最大在线完美二分匹配的最优竞争算法

针对具有iid到达的最大在线完美二部匹配问题，我们提出了一种最优竞争算法。在这个问题中，我们得到了一组已知的工人，工作类型的分布以及每对工人和工作类型的非负效用权重。在每个时间步长，都会从作业类型的分布中提取作业。到达后，必须将工作不可撤销地分配给工人，并且不能丢掉。目标是在分配所有作业后使实用程序的预期总和最大化。我们介绍了Dispatch，这是一种0.5竞争的随机算法。我们还证明了0.5竞争是最好的。工作到达时，派遣首先选择一个“首选工人”，并将该工作分配给该工人（如果有）。基于分部运输问题的最佳解决方案确定首选工人。如果首选工作人员不可用，则Dispatch会从可用工作人员中随机选择一个工作人员。