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Many MAC sub-layer protocols for supporting the use of directional antennas in ad hoc networks have been proposed. However, there remain two open issues that are yet to be resolved completely. First, in order to exploit fully the spatial diversity gains due to the use of directional antennas, it is essential to shift to the exclusive use of directional antennas for the transmission and reception of all the upper layers frames. This facilitates maximal spatial re-use and effaces the phenomenon of asymmetry in gain. Second, in the presence of mobility, the MAC protocol should incorporate mechanisms by which a node can efficiently locate and track its neighbors. We propose a new polling based MAC protocol that addresses both the issues in an integrated way. We perform analysis and extensive simulations to understand the performance of our scheme in terms of its ability to maintain connectivity, the achieved utilization efficiency, and throughput. We find that each node, on average, can achieve a per node utilization of about 80% in static and about 45% in mobile scenarios. Our protocol is seen to outperform both the traditional IEEE 802.11 MAC protocol and previously proposed protocols for use with directional antennas that provide partial solutions to solve the aforementioned problems. Finally, we also study the sensitivity of our protocol to various system parameters.