The diversity-multiplexing trade-off (DMT) of half-duplex single-relay networks is computed analytically, where all the channels in the networks are assumed to be quasi-static flat-fading channels with independent Rayleigh distributions. We have computed DMT of dynamic quantize-map-and-forward (DQMF) strategy analytically, which has the optimal DMT for half-duplex single-relay networks with local channel state information. As a result, the optimal listening time of the relay in the DQMF strategy as a function of the source-relay channel realization can also be determined using our solution.