Edge computing is aimed to support compute-intensive data-hungry interactive applications which can hardly run on resource-constrained consumer devices and may suffer from running in the cloud due to the long data transfer delay. The edge network nodes' heterogeneous and limited (compared to the cloud) capabilities make the computing task placement a challenge. In this paper, we propose a novelin-networktask placement strategy aimed at minimizing the edge network resources usage. The proposal specifically accounts fortime-limited reusablecomputing tasks, i.e., tasks whose output can be cached to serve requests from different consumers for a certain time. Caching such results, during their time validity, achieves the twofold benefit of reducing the service provisioning time and improving the edge resource utilization, by avoiding redundant computations and data exchange. The devised strategy is implemented as a network application of a Software-defined Networking Controller in charge of overseeing the edge domain. We formulate the optimal task placement through an integer linear programming problem, and we define an efficient heuristic algorithm that well approximates the solution achieved through a standard optimal solver. Achieved results show that the proposal successfully meets the targeted objectives in a wide variety of simulated scenarios, by outperforming benchmark solutions.