Network measurement is essential for assessing performance issues, identifying and locating problems. Two common strategies are the passive approach that attaches specific devices to links in order to monitor the traffic that passes through the network and the active approach that generates explicit control packets in the network for measurements. One of the key issues in this domain is to minimize the overhead in terms of hardware, software, maintenance cost and additional traffic. In this paper, we study the problem of assigning tap devices for passive monitoring and beacons for active monitoring. Minimizing the number of devices and finding optimal strategic locations is a key issue, mandatory for deploying scalable monitoring platforms. In this article, we present a combinatorial view of the problem from which we derive complexity and approximability results, as well as efficient and versatile Mixed Integer Programming (MIP) formulations.