The one-round Voronoi game

Otfried Cheong; Sariel Har-Peled; Nathan Linial; Jiří Matoušek

doi:10.1145/513400.513413

The one-round Voronoi game

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

^*Corresponding author for this work

Research output: Contribution to conference › Paper › peer-review

17 Scopus citations

Abstract

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 language	American English
Pages	97-101
Number of pages	5
DOIs	https://doi.org/10.1145/513400.513413
State	Published - 2002
Externally published	Yes
Event	Proceedings of the 18th Annual Symposium on Computational Geometry (SCG'02) - Barcelona, Spain Duration: 5 Jun 2002 → 7 Jun 2002

Conference

Conference	Proceedings of the 18th Annual Symposium on Computational Geometry (SCG'02)
Country/Territory	Spain
City	Barcelona
Period	5/06/02 → 7/06/02

Keywords

Competitive Facility Location
Voronoi diagram
Voronoi game

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10.1145/513400.513413

Cite this

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title = "The one-round Voronoi game",

abstract = "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.",

keywords = "Competitive Facility Location, Voronoi diagram, Voronoi game",

author = "Otfried Cheong and Sariel Har-Peled and Nathan Linial and Ji{\v r}{\'i} Matou{\v s}ek",

year = "2002",

doi = "10.1145/513400.513413",

language = "American English",

pages = "97--101",

note = "Proceedings of the 18th Annual Symposium on Computational Geometry (SCG'02) ; Conference date: 05-06-2002 Through 07-06-2002",

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T1 - The one-round Voronoi game

AU - Cheong, Otfried

AU - Har-Peled, Sariel

AU - Linial, Nathan

AU - Matoušek, Jiří

PY - 2002

Y1 - 2002

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 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.

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 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.

KW - Competitive Facility Location

KW - Voronoi diagram

KW - Voronoi game

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DO - 10.1145/513400.513413

M3 - Paper

AN - SCOPUS:0036368430

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EP - 101

T2 - Proceedings of the 18th Annual Symposium on Computational Geometry (SCG'02)

Y2 - 5 June 2002 through 7 June 2002

ER -

The one-round Voronoi game

Abstract

Conference

Keywords

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