A stream application may use small chunks of executable code configured to process data tuples flowing into a processing element. A scheduler allocates the processing elements to individual compute nodes or hosts for execution. However, the stream application may assign various constraints that stipulate which hosts are suitable for a particular processing element. To assign hosts to processing elements such that the constraints are satisfied, the scheduler may use hostpools associated with the processing elements. Once a host is identified that satisfies the constraints, it may be pinned at a particular index within the hostpool.