The high-definition (HD) map is a cornerstone of autonomous driving. The crowdsourcing paradigm is a cost-effective way to keep an HD map up-to-date. Current HD map crowdsourcing mechanisms aim to enhance HD map freshness within recruitment budgets. However, many overlook unique and critical traits of crowdsourcing vehicles, such as random arrival and heterogeneity, leading to either compromised map freshness or excessive recruitment costs. Furthermore, these characteristics complicate the characterization of the feasible space of the optimal recruitment policy, necessitating a method to compute it efficiently in dynamic transportation scenarios.To overcome these challenges, we propose an efficient and cost-effective vehicle recruitment (ENTER) mechanism. Specifically, the ENTER mechanism has a threshold structure and balances freshness with recruitment costs while accounting for the vehicles' random arrival and heterogeneity. It also integrates the bound-based relative value iteration (RVI) algorithm, which utilizes the threshold-type structure and upper bounds of thresholds to reduce the feasible space and expedite convergence. Numerical results show that the proposed ENTER mechanism increases the HD map company's payoff by 23.40% and 43.91% compared to state-of-the-art mechanisms that do not account for vehicle heterogeneity and random arrivals, respectively. Furthermore, the bound-based RVI algorithm in the ENTER mechanism reduces computation time by an average of 18.91% compared to the leading RVI-based algorithm.

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