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https://hdl.handle.net/10119/10302
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| 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: | https://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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