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
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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 -