Cloning Voronoi diagrams via retroactive data structures

Authors:
Matthew T. Dickerson;David Eppstein;Michael T. Goodrich
Affiliations:
Dept. of Math and Computer Sci., Middlebury College, Middlebury, Vermont;Computer Science Department, University of California, Irvine;Computer Science Department, University of California, Irvine
Venue:
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Year:
2010

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Abstract

We address the problem of replicating a Voronoi diagram V(S) of a planar point set S by making proximity queries: 1. the exact location of the nearest site(s) in S 2. the distance to and label(s) of the nearest site(s) in S 3. a unique label for every nearest site in S. In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.