  We study the problem of selecting a user equipment (UE) and a beam for each
access point (AP) for concurrent transmissions in a millimeter wave (mmWave)
network, such that the sum of weighted rates of UEs is maximized. We prove that
this problem is NP-complete. We propose two algorithms -- Markov Chain Monte
Carlo (MCMC) based and local interaction game (LIG) based UE and beam selection
-- and prove that both of them asymptotically achieve the optimal solution.
Also, we propose two fast greedy algorithms -- NGUB1 and NGUB2 -- for UE and
beam selection. Through extensive simulations, we show that our proposed greedy
algorithms outperform the most relevant algorithms proposed in prior work and
perform close to the asymptotically optimal algorithms.
