Because radio waves decay rapidly in sea water, acoustic communication is the most popular choic for underwater sensor networks. However, since the propagation speed of acoustic waves are 3 orders slower than radio waves, scheduling techniques designed for radio-based communication systems may not be suitable for underwater use. We consider how to time schedule each link in a broadcast domain once. We show that, unlike its terrestrial RF counterpart, this problem is NP complete. We then use a complete SAT solver to investigate the relation between the schedule length and the satisfiability of a given network. In radio-based communication systems, the minimum schedule length is equal to the number of transmitters located in the same broadcast domain. However, this is not the case for underwater acoustic setting. The minimum schedule length can be smaller due to the fact of nonnegligible propagation delay. Counter-intuitively, under certain circumstances, it can also be larger than the...