Computation partitioning is an important technique to improve the application performance by selectively offloading some computations from the mobile devices to the nearby edge cloud. In a dynamic environment in which the network bandwidth to the edge cloud may change frequently, the partitioning of the computation needs to be updated accordingly. The frequent updating of partitioning leads to high state migration cost between the mobile side and edge cloud. However, existing works don’t take the state migration overhead into consideration. Consequently, the partitioning decisions may cause significant network congestion and increase overall completion time tremendously. In this article, with considering the state migration overhead, we propose a set of novel algorithms to update the partitioning based on the changing network bandwidth. To the best of our knowledge, this is the first work on computation partitioning for stateful data stream applications in dynamic environments. The algorithms aim to alleviate the network congestion and minimize the make-span through selectively migrating state in dynamic edge cloud environments. Extensive simulations show our solution not only could selectively migrate state but also outperforms other classical benchmark algorithms in terms of make-span. The proposed model and algorithms will enrich the scheduling theory forstatefultasks, which has not been explored before.