In a centralized or cloud radio access network, certain portions of the digital baseband processing of a group of several radio access points are executed at a central data center. Centralizing the processing improves the flexibility, scalability, and utilization of computational assets. However, the performance depends critically on how the limited data processing resources are allocated to serve the needs of the different wireless devices. As the processing load imposed by each device depends on its allocated transmission rate and channel quality, the rate-allocation aspect of the scheduling should take into account the available computing. In this paper, two computationally aware schedulers are proposed that have the objective of maximizing the sum-rate of the system while satisfying a constraint on the offered computational load. The first scheduler optimally allocates resources and is implemented according to a water-filling algorithm. The second scheduler is suboptimal, but uses a simpler and intuitive complexity-cut-off approach. The performance of both schedulers is evaluated using an LTE-compliant system level simulator. It is found that both schedulers avoid outages that are caused by an overflow of computational load (i.e., computational outages) at the cost of a slight loss of sum-rate.