The operating system plays an important role in managing the reconfigurable hardware (RH) resources in a reconfigurable computing system to maximize system performance. These systems are becoming increasingly more complex, with multi-core CPUs and multi-tasking applications, each containing multiple kernels of computation that could be accelerated in RH. In such a system, the dynamic allocation of RH resources also becomes increasingly difficult. In this paper we examine one of the important issues a scheduler may encounter: the performance benefits of accelerating a particular kernel in an application may be enhanced by also accelerating other kernels in the application. We show that a scheduler that ignores these interdependencies will not always find the best allocation. We also propose a new RH scheduler designed specifically to handle these interdependencies, improving system performance.