Serverless computing is a novel cloud computing paradigm enabling flexible, cost-efficient and fine-granular development of cloud-native applications, although without any guarantees on scheduling or execution times. Thus, various high-level solutions have been proposed in recent years to find proper configurations of individual FaaS functions, while considering user-given QoS requirements. However, the ever-increasing complexity of invocation patterns among stateless functions, externalized management of intermediate states, and diverse public cloud resources pose new challenges to the composition of highly data-intensive serverless applications. In this paper, we fill this gap by proposing novel algorithms based on the emerging function fusion technique, along with the related cost/performance models of composite functions supporting implicit instance parallelization and internal state propagation. We prove the NP-completeness of the underlying latency-constrained tree partitioning problem, and design a bicriteria approximation scheme and a greedy heuristic to derive cost-efficient deployment configurations in polynomial time. With the help of extensive simulations using synthetic call graphs generated from public cloud traces, we demonstrate the applicability and superior runtime performance of our proposed methods compared to state-of-the-art solutions. In addition, we showcase that further cost-reduction of up to 3–6 % can be achieved compared to the optimal partitioning with the allowance of tolerable latency violations.