There is a growing demand for live, on-the-fly processing of increasingly large amounts of data. In order to ensure the timely and reliable processing of streaming data, a variety of distributed stream processing architectures and platforms have been developed, which handle the fundamental tasks of (dynamically) assigning processing tasks to the currently available physical resources and routing streaming data between these resources. However, while there are plenty of platforms offering such functionality, the theory behind it is not well understood. In particular, it is unclear how to best allocate the processing tasks to the given resources. In this paper, we establish a theoretical foundation by formally defining a task allocation problem for distributed stream processing, which we prove to be NP-hard. Furthermore, we propose an approximation algorithm for the class of series-parallel decomposable graphs, which captures a broad range of common stream processing applications. The algorithm achieves a constant-factor approximation under the assumptions that the number of resources scales at least logarithmically with the number of computational tasks and the computational cost of the tasks dominates the cost of communication.

Extended Version of the work published in the proceedings of IEEE International Conference on Computer Communications (INFOCOM), 10-15 April 2016, San Francisco, USA