Discrete & Computational Geometry

, Volume 31, Issue 1, pp 125–138 | Cite as

The One-Round Voronoi Game

  • Otfried Cheong
  • Sariel Har-Peled
  • Nathan Linial
  • Jirí Matousek


In the one-round Voronoi game, the first player chooses an n-point set W in a square Q, and then the second player places another n-point set B into Q. The payoff for the second player is the fraction of the area of Q occupied by the regions of the points of B in the Voronoi diagram of W \cup B. We give a (randomized) strategy for the second player that always guarantees him a payoff of at least ½ + α, for a constant α > 0 and every large enough n. This contrasts with the one-dimensional situation, with Q=[0,1], where the first player can always win more than ½.


Voronoi Diagram 
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Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB EindhovenThe Netherlands
  2. 2.Department of Computer Science, University of Illinois, 1304 W. Springfield Ave., Urbana, IL 61801USA
  3. 3.Institute of Computer Science, Hebrew University, Jerusalem 91904Israel
  4. 4.Department of Applied Mathematics and Institute of Theoretical Computer Science (ITI), Charles University, Malostranské nám. 25, 118 00 Praha 1Czech Republic

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