The Voronoi game on graphs and its complexity
Author(s)Teramoto, Sachio; Demaine, Erik D.; Uehara, Ryuhei
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal of Graph Algorithms and Applications
Department of Computer Science, Brown University
Teramoto, Sachio, Erik D. Demaine, and Ryuhei Uehara. “The Voronoi Game on Graphs and Its Complexity.” Journal of Graph Algorithms and Applications 15, no. 4 (2011): 485–501.
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