TY - JOUR

T1 - The One-Round Voronoi Game

AU - Cheong, Otfried

AU - Har-Peled, Sariel

AU - Linial, Nathan

AU - Matoušek, Jiří

PY - 2004/1

Y1 - 2004/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1142300712&partnerID=8YFLogxK

U2 - 10.1007/s00454-003-2951-4

DO - 10.1007/s00454-003-2951-4

M3 - Article

AN - SCOPUS:1142300712

SN - 0179-5376

VL - 31

SP - 125

EP - 138

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 1

ER -