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This paper proposes a time-efficient mechanism to decrease the on-line computing time of solving the joint unmanned aerial vehicle base station (UAV-BS) deployment and user/sensor association (UDUA) problem aiming at maximizing the downlink sum transmission throughput. The joint UDUA problem is decoupled into two sub-problems: one is the user association sub-problem, which gets the optimal matching strategy between aerial and ground nodes for certain UAV-BS positions; and the other is the UAV-BS deployment sub-problem trying to find the best position combination of the UAV-BSs that make the solution of the first sub-problem optimal among all the possible position combinations of the UAV-BSs. In the proposed mechanism, we transform the user association sub-problem into an equivalent bipartite matching problem and solve it using the Kuhn-Munkres algorithm. For the UAV-BS deployment sub-problem, we theoretically prove that adopting the best UAV-BS deployment strategy of a previous user distribution for each new user distribution will introduce little performance decline compared with the new user distribution's ground true best strategy if the two user distributions are similar enough. Based on our mathematical analyses, the similarity level between user distributions is well defined and becomes the key to solve the second sub-problem. Numerical results indicate that the proposed UDUA mechanism can achieve near-optimal system performance in terms of average downlink sum transmission throughput and failure rate with enormously reduced computing time compared with benchmark approaches.