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In this paper, we study the data broadcast issue in wireless networks with directional antennas. We are given an Access Point(AP) and a set of clients served by the AP. Our task is to schedule the transmission of AP by using directional antennas such that the total delay for all clients to receive a broadcast packet is minimized. Directional antennas allow transmission energy to be concentrated on a narrow range along a direction, which can significantly increase the data rate of clients. However, there is a difficult issue in using directional antennas for data broadcasting. If the AP transmits the signals through a single lobe, the data rate of the clients covered by this lobe can be high but it takes more number of transmissions to cover all clients. On the other hand, if the AP transmits the signals through multiple lobes, it takes less number of transmissions for all clients to receive the data, but the signal strength decreases and the data rate drops. We study this tradeoff between the number of transmissions and the data rate. We prove that the data broadcasting problem is NP-hard and we propose a two-phase method to solve the problem. In the first phase, we use singlelobes to cover all clients such that the total transmission delay is minimized. In the second phase, we group these single-lobes into a set of multi-lobes. The goal is again to minimize the total transmission delay. The solution for each subproblem is optimal. Simulation results show significant improvements of performance compared with state of the art algorithms.