Current IP based networks support a wide range of delay-sensitive applications such as live video streaming of network gaming. Providing an adequate quality of experience to these applications is of paramount importance for a network provider. The offered services are often regulated by tight Service Level Agreements (SLAs) that needs to be continuously monitored. Since the first step to guarantee a metric is to measure it, delay measurement becomes a fundamental operation for a network provider. In many cases, the operator needs to measure the delay on all network links. We refer to the collection of all link delays as the Link Delay Vector (LDV). Typical solutions to collect the LDV impose a substantial overhead on the network. In this paper, we propose a solution to measure the LDV in real-time with a low-overhead approach. In particular, we inject some flows into the network and infer the LDV based on the delay of those flows. To this end, the monitoring flows and their paths should be selected minimizing the network monitoring overhead. In this respect, the challenging issue is to select a proper combination of flows such that by knowing their delay it is possible to solve a set of a linear equation and obtain a unique LDV. This combination of monitoring flows should be optimal according to some criteria and should meet some feasibility constraints. We first propose a mathematical formulation to select the optimal combination of flows, in form of Integer Linear Programming (ILP) problem. Then we develop a heuristic algorithm to overcome the high computational complexity of existing ILP solvers. As a further step, we propose a meta-heuristic algorithm to solve the abovementioned equations and infer the LDV. The challenging part of this step is the volatility of link delays. The proposed solution is evaluated over real-world emulated network topologies using the Mininet network emulator. Emulation results show the accuracy of the proposed solution with a negligible networking overhead in a real-time manner.