In this paper we consider the operator mapping problem for in-networkstream processing applications. In-network stream processing consists inapplying a tree of operators in steady-state to multiple data objects thatare continually updated at various locations on a network. Examples ofin-network stream processing include the processing of data in a sensornetwork, 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 applicationbuy purchasing processing servers with various costs and capabilities.The objective is to minimize the cost of the platform while ensuringthat the application achieves a minimum ste...