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For mobile ad hoc networks, network-wide broadcast is a critical network layer function supporting route discovery and maintenance in many unicast and multicast protocols. A number of broadcast schemes have been proposed; however, almost all of them assume the usage of omnidirectional antennas and focus on broadcast overhead in terms of the number of forwarding nodes. Directional antennas have narrow beams and can potentially reduce broadcast overhead in terms of the ratio of the number of received duplicate packets to the number of nodes that receive broadcast packets. In this paper, we propose to map probability-based directional and omnidirectional broadcast to bond and site percolation, respectively, and describe a collection of directional antenna-based broadcast schemes for mobile ad hoc networks. A thorough and comparative simulation study is conducted to demonstrate the efficiency of the proposed schemes.