With the increase in both the model size and dataset size of distributed training (DT) tasks, communication between the workers and parameter servers (PSs) in a cluster has become a bottleneck. In-network aggregation (INA) enabled by programmable switches has been proposed as a promising solution to alleviate the communication bottleneck. However, existing works focused on in-network aggregation implementation based on simple DT placement and fixed routing policies, which may lead to a large communication overhead and inefficient use of resources (e.g., storage, computing power and bandwidth). In this paper, we propose PARING, the first-of-its-kind INA approach that jointly optimizes DT task placement and routing in order to reduce traffic volume and minimize communication time. We formulate the problem as a nonlinear multi-objective mixed-integer programming problem, and prove its NP-Hardness. Based on the concept of Steiner trees, an algorithm with bounded approximation factors is proposed for this problem. Large-scale simulations show that our algorithm can reduce communication time by up to 81.0% and traffic volume by up to 19.1% compared to the state-of-the-art algorithms.