Power Diagram Detection with Applications to Information Elicitation

Power diagrams, a type of weighted Voronoi diagram, have many applications throughout operations research. We study the problem of power diagram detection: determining whether a given finite partition of $${\mathbb {R}}^d$$ R d takes the form of a power diagram. This detection problem is particularly prevalent in the field of information elicitation, where one wishes to design contracts to incentivize self-minded agents to provide honest information. We devise a simple linear program to decide whether a polyhedral cell complex can be described as a power diagram. For positive instances, a representation of the cell complex as a power diagram is returned. Further, we discuss applications to property elicitation, peer prediction, and mechanism design, where this question arises. Our model can efficiently decide the question for complexes of $${\mathbb {R}}^d$$ R d or of a convex subset thereof. The approach is based on the use of an alternative representation of power diagrams and invariance of a power diagram under uniform scaling of the parameters in this representation.