The capacity of a wireless network could be considerably improved by employing directional antennas that are capable of illuminating multiple beams toward different directions. However, more beams from the same BS may lead to stronger inter-cell interference. In this paper, we consider coordinated beam scheduling schemes to mitigate the inter-cell interference. We first formulate this problem as a combinatorial optimization problem. We then reveal that the complexity of this problem hinges upon a single scalar termed as degree of constraint (DoC), which is related to the degree of conflict a beam is subject to. If the DoC is at least three, the general beam scheduling problem is NP-hard. If DoC is smaller than three, which corresponds to a relevant subclass of the beam scheduling problem arising in practice, this problem can be solved in polynomial time. We propose an optimal beam scheduling algorithm based on the auction method to this particular subclass of problem. This algorithm is of low complexity and is well suited for distributed implementations. We then extend the auction algorithm to solve the general multi-cell beam scheduling problem. The performance of the proposed algorithms is finally assessed through extensive simulation studies.