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A variety of real-world applications share the property that data arrives inform of transient streams. Data stream management systems (DSMS) provide convenient solutions to the problem of processing continuous queries on those streams. Within a DSMS, the scheduling of the queries and their operators has proved to be of utmost importance. Previous approaches addressing this issue can be divided into two categories: either each operator runs in its own thread or all operators, combined in one query graph, run in a single thread. Both approaches suffer from severe drawbacks concerning the thread overhead on the one hand and the stalls due to expensive operators on the other hand. To overcome these drawbacks, we propose in this work a hybrid approach that flexibly assigns threads to subgraphs of the query graph. We complement this approach with a suitable strategy to determine these subgraphs. The results of an experimental study substantiate the feasibility of our approach and its superiority to previous approaches.