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In this paper, we present a TDMA-based medium access control (MAC) algorithm specifically designed for link scheduling in a mobile wireless network composed of nodes equipped with directional antennas, each of which is capable of forming a single beam in an arbitrary direction. Using the MAC algorithm, a node negotiates slot reservations with a neighbor based only on information about the two nodes' available slots and the expected traffic load. We provide simulation results illustrating the performance of this algorithm in terms of goodput, delay, and success of reservations, and we also compare its performance against that of a CSMA/CA MAC algorithm designed for use with directional antennas. Furthermore, we show that if the capabilities of each antenna are expanded to include formation of multiple simultaneous beams, then the MAC algorithm can be extended to efficiently negotiate reservations for multicast transmissions.