The One-Round Voronoi Game

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

47 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 (randomized) strategy for the second player that always guarantees him a payoff of at least 1/2 + 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 1/2.

Original languageAmerican English
Pages (from-to)125-138
Number of pages14
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Jan 2004


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