how can one construct a finite set of points in the euclidean plane from its Voronoi Diagram and, what is the complexity of the problem?



Algorithm for Reconstructing Point Sites from a Voronoi Diagram
This is a well studied problem and there are a couple of algorithms, for example using linear programming. For an overview take a recent reference, for example:


[Fitting Voronoi Diagrams to Planar Tesselations](https://arxiv.org/abs/1308.5550) by Greg Aloupis, Hebert Pérez-Rosés, Guillermo Pineda-Villavicencio, Perouz Taslakian, Dannier Trinchet


