This paper investigates the operator mapping problem for in-network stream-processing applications. In-network stream-processing amounts to applying one or more trees of operators in steady-state, to multiple data objects that are continuously updated at different locations in the network. The goal is to compute some final data at some desired rate. Different operator trees may share common subtrees. Therefore, it may be possible to reuse some intermediate results in different application trees. The first contribution of this work is to provide complexity results for different instances of the basic problem, as well as integer linear program formulations of various problem instances. The second second contribution is the design of several p...