2017年
Sankaku-Tori: An old Western-Japanese game played on a point set
Journal of Information Processing
- ,
- ,
- ,
- ,
- ,
- ,
- 巻
- 25
- 号
- 8
- 開始ページ
- 708
- 終了ページ
- 715
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
We study a combinatorial game named "sankaku-tori" in Japanese, which means "triangle-taking" in English. It is an old pencil-and-paper game for two players played in Western Japan. The game is played on points on the plane in general position. In each turn, a player adds a line segment to join two points, and the game ends when a triangulation of the point set is completed. The player who completes more triangles than the other wins. In this paper, we formalize this game and investigate three restricted variants of this game. We first investigate a solitaire variant; for a given set of points and line segments with two integers t and k, the problem asks if you can obtain t triangles after k moves. We show that this variant is NP-complete in general. The second variant is the standard two player version, but the points are in convex position. In this case, the first player has a nontrivial winning strategy. The last variant is a natural extension of the second one; we have the points in convex position but one point inside. Then, it turns out that the first player has no winning strategy.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.25(2017) (online)DOI http://dx.doi.org/10.2197/ipsjjip.25.708------------------------------We study a combinatorial game named "sankaku-tori" in Japanese, which means "triangle-taking" in English. It is an old pencil-and-paper game for two players played in Western Japan. The game is played on points on the plane in general position. In each turn, a player adds a line segment to join two points, and the game ends when a triangulation of the point set is completed. The player who completes more triangles than the other wins. In this paper, we formalize this game and investigate three restricted variants of this game. We first investigate a solitaire variant; for a given set of points and line segments with two integers t and k, the problem asks if you can obtain t triangles after k moves. We show that this variant is NP-complete in general. The second variant is the standard two player version, but the points are in convex position. In this case, the first player has a nontrivial winning strategy. The last variant is a natural extension of the second one; we have the points in convex position but one point inside. Then, it turns out that the first player has no winning strategy.------------------------------This is a preprint of an article intended for publication Journal ofInformation Processing(JIP). This preprint should not be cited. Thisarticle should be cited as: Journal of Information Processing Vol.25(2017) (online)DOI http://dx.doi.org/10.2197/ipsjjip.25.708------------------------------
- リンク情報
-
- CiNii Articles
- http://ci.nii.ac.jp/naid/170000148848
- CiNii Books
- http://ci.nii.ac.jp/ncid/AN00116647
- URL
- http://id.nii.ac.jp/1001/00182922/
- ID情報
-
- ISSN : 1882-7764
- CiNii Articles ID : 170000148848
- CiNii Books ID : AN00116647