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Vehicular ad hoc networks have several characteristics that distinguish them from other ad hoc networks. Among those is the rapid change in topology due to traffic jams, which also disturbs the homogeneous distribution of vehicles on the road. For this reason, a dynamic transmission range is more effective in maintaining the connectivity while minimizing the adverse effects of a high transmission power. This paper proposes a scheme that allows vehicles to estimate the local density and distinguish between the free-flow and the congested traffic phases. The density estimate is used to develop a dynamic transmission-range-assignment (DTRA) algorithm that sets a vehicle transmission range dynamically according to the local traffic conditions. Simulations of several road configurations validate the quality of the local density estimation and show that the DTRA algorithm is successful in maintaining the connectivity in highly dynamic networks.