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Power Diagram Detection with Applications to Information Elicitation

  • Steffen BorgwardtEmail author
  • Rafael M. Frongillo
Article
  • 92 Downloads

Abstract

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 \({\mathbb {R}}^d\) 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 \({\mathbb {R}}^d\) 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.

Keywords

Power diagram Information elicitation Linear programming 

Mathematics Subject Classification

90C05 90C90 91B06 62C05 

Notes

Acknowledgements

We thank Ian Kash for helpful discussions on the applications of our results. Borgwardt gratefully acknowledges support through the Collaboration Grant for Mathematicians, Polyhedral Theory in Data Analytics, of the Simons Foundation, and Frongillo through the Computer and Information Science and Engineering Research Initiation Initiative Grant, Characterization and Complexity of Information Elicitation, of the National Science Foundation.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Colorado DenverDenverUSA
  2. 2.University of Colorado BoulderBoulderUSA

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