Multimedia applications, like, e.g., 3-D games and video decoders, are typically composed of communicating tasks. Their target embedded computing platforms (e.g., TI OMAP3, IBM Cell) contain multiple heterogeneous processing elements. At application design-time, it is often unknown which applications will execute simultaneously. Hence, resource assignment decisions need to be made by a run-time manager. Run-time assignment of these communicating tasks onto the communication and computation resources of such a multiprocessor platform is a challenging task. In the presence of fine-grain reconfigurable hardware processing elements, the run-time manager also needs to consider the creation of a so-called configuration hierarchy. Instead of executing a dedicated hardware task, the fine-grain reconfigurable hardware fabric hosts a programmable softcore block that, in turn, executes the task functionality. Hence, the next challenge for run-time management is to efficiently handle a configuration hierarchy. This paper details a run-time task assignment heuristic that performs fast and efficient task assignment in a multiprocessor system-on-chip containing fine-grain reconfigurable hardware tiles. In addition, this algorithm is capable of managing a configuration hierarchy. We show that being capable of handling a configuration hierarchy significantly improves the task assignment performance (i.e., success rate and assignment quality). In several cases, adding a configuration hierarchy improves the assignment success rate of the assignment heuristic by 20%.