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Using directional antennas to conserve bandwidth and energy consumption in ad hoc wireless networks has attracted much attention of the research community in recent years. However, limited research has focused on applying directional antennas to broadcasting. We devise a link reduction (LR) based broadcasting protocol for ad hoc wireless networks using directional antennas. LR outperforms most existing omnidirectional and directional broadcasting schemes in the sense that its normalized transmission cost and redundancy are significantly reduced, and consequently it is more bandwidth and energy- efficient. Based on 2-hop neighborhood information, LR relies on no location or angle-of-arrival (AOA) information. LR is a localized protocol and it achieves full delivery in ideal networks. Simulation is conducted in ideal networks where packet collision, channel contention, or node mobility is avoided.