The one-round Voronoi game

Otfried Cheong*, Sariel Har-Peled, Nathan Linial, Jiří Matoušek

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

18 Scopus citations


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 ∪ B. We give a strategy for the second player that always guarantees him a payoff of at least 1/2 + α, for a constant α > 0 independent of n. This contrasts with the one-dimensional situation, with Q [0, 1], where the first player can always win more than 1/2.

Original languageAmerican English
Number of pages5
StatePublished - 2002
Externally publishedYes
EventProceedings of the 18th Annual Symposium on Computational Geometry (SCG'02) - Barcelona, Spain
Duration: 5 Jun 20027 Jun 2002


ConferenceProceedings of the 18th Annual Symposium on Computational Geometry (SCG'02)


  • Competitive Facility Location
  • Voronoi diagram
  • Voronoi game


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