肾脏交换和无尽的路径：关于利他捐赠者的最佳使用
Kidney exchange and endless paths: On the optimal use of an altruistic donor
摘要：
我们考虑一个经过充分研究的在线随机图模型肾脏交换，其中代表患者-供体对的节点随着时间的推移到达，并且有向边缘的概率为p。我们假设存在单个利他捐助者，其作为该图中的有向路径捐赠的起始节点。算法问题是选择进行哪些捐赠，以及何时进行，以最大限度地减少患者在接受肾脏之前必须等待的时间。我们通过（1）提供有效的（实际上，线性时间）算法的最佳O（1/p）预期等待时间，（2）表明这些算法中的一些实际上提供了保证所有患者的O（1/p）等待时间{ \em以高概率}，（3）简化了以前对这个问题的分析，以及（4）将结果扩展到多个利他捐赠者的情况。
英文摘要：
We consider a well-studied online random graph model for kidney exchange, where nodes representing patient-donor pairs arrive over time, and the probability of a directed edge is p. We assume existence of a single altruistic donor, who serves as a start node in this graph for a directed path of donations. The algorithmic problem is to select which donations to perform, and when, to minimize the amount of time that patients must wait before receiving a kidney. We advance our understanding of this setting by (1) providing efficient (in fact, linear-time) algorithms with optimal O(1/p) expected waiting time, (2) showing that some of these algorithms in fact provide guarantees to all patients of O(1/p) waiting time {\em with high probability}, (3) simplifying previous analysis of this problem, and (4) extending results to the case of multiple altruistic donors.
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