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In this paper, we propose a lightweight proactive routing protocol, called adaptive multitier routing (AMR), for vertical traffic in tactical networks. By adopting an asymmetric tree-like network topology, AMR minimizes the control overhead in the network as well as the computational complexity on intermediate nodes. Such tree topology provides both network connectivity and traffic distribution information. By routing via the tree topology, AMR automatically adapts to the network mobility and traffic dynamics. Using different routing trees for distinct traffic classes, AMR can provide service differentiation at the network layer. Simulation results show that the proposed routing protocol provides reliable data delivery, reacts dynamically to network changes and provides network layer service differentiation with low overhead.