Link observability without path enumeration: A revisit

In this paper we revisit the following link observability problem: Determine the smallest subset of links in a traffic network for counting sensor installation, in such a way that it becomes possible to infer the flows on all remaining links. While a solution methodology has already been proposed in the literature, unfortunately, path enumeration was required which is infeasible for large-scale networks. In this work, we present a reformulation of the link observability problem, requiring only node enumeration. Using this node-based approach, we prove a conjecture made in the literature by deriving an explicit relationship between the number of nodes and links in a transportation network, and the minimum number of sensors to install in order to be able to infer all link flows. Numerical results are reported and discussed.