: Data stream processing systems enable querying continuous data without first storing it. Data stream queries may combine data from distributed data sources like different sensors in an environmental sensing application. This suggests distributed query processing. Thus the amount of transferred data can be reduced and more processing resources are available. However, distributed query processing on probably heterogeneous platforms complicates query optimization. This article investigates query optimization through operator graph changes and its interaction with operator placement on heterogeneous distributed systems. Pre-distribution operator graph changes may prevent certain operator placements. Thereby the resource consumption of the query execution may unexpectedly increase. Based on the operator placement problem modeled as a task assignment problem (TAP), we prove that it is NP-hard to decide in general whether an arbitrary operator graph change may negatively influence the bes...