We study generalizations of online bipartite matching in which each arriving vertex (customer) views a ranked list of offline vertices (products) and matches to (purchases) the first one they deem acceptable. The number of products that the customer has patience to view can be stochastic and dependent on the products seen. We develop a framework that views the interaction with each customer as an abstract resource consumption process, and derive new results for these online matching problems under the adversarial, non-stationary, and IID arrival models, assuming we can (approximately) solve the product ranking problem for each single customer. To that end, we show new results for product ranking under two cascade-click models: an optimal algorithm when each item has its own hazard rate for making the customer depart, and a 1/2-approximate algorithm when the customer has a general item-independent patience distribution. We also present a constant-factor 0.027-approximate algorithm in a new model where items are not initially available and arrive over time. We complement these positive results by presenting three additional negative results relating to these problems.

翻译：我们研究在线二分匹配的推广问题，其中每个到达的顶点（客户）浏览离线顶点（产品）的排序列表，并与第一个认为可接受的产品匹配（购买）。客户愿意查看的产品数量可能是随机的，并取决于所看到的产品。我们开发了一个框架，将每个客户的互动视为一个抽象的资源消耗过程，并在对抗性、非平稳和独立同分布到达模型下为这些在线匹配问题推导了新结果，前提是我们能够（近似地）求解每个单个客户的产品排序问题。为此，我们展示了两种级联点击模型下的产品排序新结果：当每个物品具有导致客户离开的独立风险率时的最优算法，以及当客户具有独立于物品的一般耐心分布时的1/2近似算法。我们还提出了一种新模型下的常数因子0.027近似算法，其中物品初始不可用并随时间到达。我们通过呈现与这些问题相关的三个额外负面结果来补充这些正面结果。