Journal of Graph Algorithms and Applications
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The Voronoi game on graphs and its complexity
Vol. 15, no. 4, pp. 485-501, 2011. Regular paper.
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 is intractable 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.
Submitted: May 2009.
Reviewed: October 2009.
Revised: July 2011.
Accepted: August 2011.
Final: August 2011.
Published: August 2011.
Communicated by Henk Meijer