In this paper we consider the operator mapping problem for in-network stream processing applications. In-network stream processing consists in applying a tree of operators in steady-state to multiple data objects that are continually updated at various locations on 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. We study the operator mapping problem in a ``constructive'' scenario, i.e., a scenario in which one builds a platform dedicated to the application buy purchasing processing servers with various costs and capabilities. The objective is to minimize the cost of the platform while ensuring that the application achieves a minimum steady-state throughput. The first contribution of this paper is the formalization of a set of relevant operator-placement problems as linear programs, and a proof that even simple versions of the problem are NP-complete. Our second contribution is the design of several polynomial time heuristics, which are evaluated via extensive simulations and compared to theoretical bounds for optimal solutions.