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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/10302

Title: The Voronoi game on graphs and its complexity
Authors: Teramoto, Sachio
Demaine, Erik D.
Uehara, Ryuhei
Keywords: graph algorithms
Voronoi Game
NP-completeness
PSPACE-completeness
Issue Date: 2011-08
Publisher: Journal of Graph Algorithms and Applications
Magazine name: Journal of Graph Algorithms and Applications
Volume: 15
Number: 4
Start page: 485
End page: 501
Abstract: The Voronoi game is a two-person game which is a model for a competitive facility location. The game is played on a continuous domain, and only two special cases (one-dimensional case and one-round case) are well investigated. We introduce the discrete Voronoi game in which the game arena is given as a graph. We first analyze the game when the arena is a large complete k-ary tree, and give an optimal strategy. When both players play optimally, the first player wins when k is odd, and the game ends in a tie for even k. Next we show that the discrete Voronoi game isintractable in general. Even for the one-round case in which the strategy adopted by the first player consist of a fixed single node, deciding whether the second player can win is NP-complete. We also show that deciding whether the second player can win is PSPACE-complete in general.
Rights: Copyright (C) 2011 Journal of Graph Algorithms and Applications. Sachio Teramoto, Erik D. Demaine, and Ryuhei Uehara, Journal of Graph Algorithms and Applications, 15(4), 2011, 485-501.
URI: http://hdl.handle.net/10119/10302
Material Type: publisher
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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