By relying on small sized and massively distributed infrastructures, the Edge computing paradigm aims at supporting the low latency and high bandwidth requirements of the next generation services that will leverage IoT devices (e.g., video cameras, sensors). To favor the advent of this paradigm, management services, similar to the ones that made the success of Cloud computing platforms, should be proposed. However, they should be designed in order to cope with the limited capabilities of the resources that are located at the edge. In that sense, they should mitigate as much as possible their footprint. Among the different management services that need to be revisited, we investigate in this paper the monitoring one. Monitoring functions tend to become compute-, storage-and network-intensive, in particular because they will be used by a large part of applications that rely on real-time data. To reduce as much as possible the footprint of the whole monitoring service, we propose to mutualize identical processing functions among different tenants while ensuring their quality-of-service (QoS) expectations. We formalize our approach as a constraint satisfaction problem and show through micro-benchmarks its relevance to mitigate compute and network footprints.