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Current vehicles are equipped with a number of environmental sensors to improve safety and quality of life for passengers. Many researchers have shown that these sensors can also be exploited for opportunistic crowd-sensing. Useful new services can be developed on top of these data, like urban surveillance of Smart Cities. The spatio-temporal sensing coverage achievable with Vehicular Crowd-Sensing (VCS), however, is an open issue, since vehicles are not uniformly distributed over the road network, undermining the quality of potential services based on VCS data. In this paper, we present an evolution of the standard A ∗ routing algorithm, meant to increase VCS coverage by selecting a route in a random way among all those satisfying a parametric constraint on the total cost of the path. The proposed solution is based on an edge-computing paradigm, not requiring a central coordination but rather leveraging the computational resources available on-board, significantly reducing the back-end infrastructure costs. The proposed solution has been empirically evaluated on two public datasets of 450,000 real taxi trajectories from two cities, San Francisco and Porto, characterized by a very different road network topology. Results show sensible improvements in terms of achievable spatio-temporal sensing coverage of probe vehicles. [ABSTRACT FROM AUTHOR]