We consider the operator mapping problem for in-network stream processing, i.e., the application of a tree of operators in steady-state to multiple data objects that are continuously updated at various locations in a network. Examples of in-network stream processing include the processing of data in a sensor network, or of continuous queries on distributed relational databases. Our aim is to provide the user a set of processors that should be bought or rented in order to ensure that the application achieves a minimum steady-state throughput, and with the objective of minimizing platform cost. We prove that even the simplest variant of the problem is NP-hard, and we design several polynomial time heuristics, which are evaluated via extensive simulations and compared to theoretical bounds.