The acoustic propagation speed under water poses significant challenges to the design of underwater sensor networks and their medium access control protocols. Similar to the air, scheduling transmissions under water has significant impact on throughput, energy consumption, and reliability. In this paper we present an extended set of simplified scheduling constraints which allows easy scheduling of underwater acoustic communication. We also present two algorithms for scheduling communications, i.e. a centralized scheduling approach and a distributed scheduling approach. The centralized approach achieves the highest throughput while the distributed approach aims to minimize the computation and communication overhead. We further show how the centralized scheduling approach can be extended with transmission dependencies to reduce the end-to-end delay of packets. We evaluate the performance of the centralized and distributed scheduling approaches using simulation. The centralized approach outperforms the distributed approach in terms of throughput, however we also show the distributed approach has significant benefits in terms of communication and computational overhead required to setup the schedule. We propose a novel way of estimating the performance of scheduling approaches using the ratio of modulation time and propagation delay. We show the performance is largely dictated by this ratio, although the number of links to be scheduled also has a minor impact on the performance.