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Cloud resources can be dynamically provisioned according to application-specific requirements and are payed on a per-use basis. This gives rise to a new concept for parallel processing: Elastic parallel computations. However, it is still an open research question to which extent parallel applications can benefit from elastic scaling, which requires resource adaptation at runtime and corresponding coordination mechanisms. In this work, we analyze how to address these system-level challenges in the context of developing and operating elastic parallel tree search applications. Based on our findings, we discuss the design and implementation of TASKWORK, a cloud-aware runtime system specifically designed for elastic parallel tree search, which enables the implementation of elastic applications by means of higher-level development frameworks. We show how to implement an elastic parallel branch-and-bound application based on an exemplary development framework and report on our experimental evaluation that also considers several benchmarks for parallel tree search.