In ad hoc wireless networks, nodes are typically powered by batteries. Therefore saving energy has become a very important objective, and different algorithms have been proposed to achieve power efficiency during the routing process. Directional antenna has been used to further decrease transmission energy as well as to reduce interference. In this paper, we discuss five algorithms for routing tree construction that take advantage of directional antenna, i.e, Reverse-Cone-Pairwise (RCP), Simple-Linear (SL), Linear-Insertion (LI), Linear-Insertion-Pairwise (LIP), and a traditional approximation algorithm for the travelling salesman problem (TSP). Their performances are compared through a simulation study. Key words: ad hoc wireless network, directional antenna, energy-efficient routing, transmission power, travelling salesman problem (TSP) PACS: