Reconstruction of planar graphs from their centered triangulations in some spatio-relational models

In this paper we continue the investigation of an interoperability problem and its complexity in connection with spatio-relational database models. The result, however, is also interesting from the point of view of graph theory, since the main result is that there is a linear-time algorithm for deciding whether a given triangulation can be seen as a centered triangulation of a certain planar graph.