Minimum Surgical Probing with Convexity Constraints

Toni Böhnlein, Niccolò Di Marco, Andrea Frosini

Abstract: We consider a tomographic problem on graphs, called Minimum Surgical Probing, introduced by Bar-Noy et al. [2]. Each vertex \(v \in V\) of a graph \(G = (V,E)\) is associated with an (unknown) label \(\ell _v\). The outcome of probing a vertex v is \(\mathcal{P}_v = \sum _{u \in N[v]} \ell _u\), where N[v] denotes the closed neighborhood of v. The goal is to uncover the labels given probes \(\mathcal{P}_v\) for all \(v \in V\). For some graphs, the labels cannot be determined (uniquely), and the use of surgical probes is permitted but must be minimized. A surgical probe at vertex v returns \(\ell _v\).