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Motivated by applications from ride-sharing and kidney exchange, we study the problem of matching agents who arrive at a marketplace over time and leave after d time periods. Agents can only be matched while they are present in the marketplace. Each pair of agents can yield a different match value, and the planner's goal is to maximize the total value over a finite time horizon. First we study the case in which vertices arrive in an adversarial order. We provide a randomized 1 /4-competitivedoi:10.1145/3328526.3329573 dblp:conf/ec/AshlagiBDJSS19 fatcat:uzevnr2hqrhollee7ian4s6oa4