We study a dynamic non-bipartite matching problem. There is a fixed set of agent types, and agents of a given type arrive and depart according to type-specific Poisson processes. The value of a match is determined by the types of the matched agents. We present an online algorithm that is (1/6)-competitive with respect to the value of the optimal-in-hindsight policy, for arbitrary weighted graphs. This is the first result to achieve a constant competitive ratio when both arrivals and departures are random and unannounced. Our algorithm treats agents heterogeneously, interpolating between immediate and delayed matching in order to thicken the market while still matching valuable agents opportunistically.

中文翻译：

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具有异质到达率和离站率的动态加权匹配

我们研究了动态的非二分匹配问题。有一组固定的座席类型，给定类型的座席会根据特定于类型的泊松过程到达和离开。匹配的值由匹配代理的类型决定。对于任意加权图，我们提出一种在线算法，该算法相对于事后最优策略的值具有（1/6）竞争性。这是在到达和离开都是随机且未经通知的情况下实现恒定竞争率的第一个结果。我们的算法对代理进行异类处理，在立即匹配和延迟匹配之间进行插值，以扩大市场，同时仍可机会地匹配有价值的代理。