Near real-time monitoring and control of critical infrastructure is essential for the operation and management of cities in a world that is, today, more complex and interconnected than ever. Such an infrastructure can be represented as complex networks an some of their related indices and statistics, many of them based on the shortest paths, play a pivotal role in the decision making for public services such as internet, energy or water. Particularly, the literature has shown that shortest paths are key for resilience and criticality assessment in a water distribution systems (WDS). This paper proposes a procedure to speed-up the computation of shortest paths in a WDS, as it can straightforwardly benefit any critical infrastructure. The proposal is based on a reduced dimension of a complex network representing any critical infrastructure. Despite the consequent decrease in the number of all possible paths in the network, the main advantage and novelty of this proposal is to continue finding the exact solution for the shortest paths. Experimental results show that the procedure brings a computational-time reduction consistently over 50% and up to 90% in some cases. In addition, the paper reveals how the use of shortest paths benefits WDS operation and management, as well as playing a key role in near real-time contamination detection and leakage control.