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http://hdl.handle.net/10119/15060
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| Title: | Sankaku-tori: An Old Western-Japanese Game Played on a Point Set |
| Authors: | Horiyama, Takashi
Iizuka, Takashi
Kiyomi, Masashi
Okamoto, Yoshio
Uehara, Ryuhei
Uno, Takeaki
Uno, Yushi
Yamauchi, Yukiko |
| Keywords: | Combinatorial game
Sankaku-tori
NP-complete |
| Issue Date: | 2017 |
| Publisher: | Information Processing Society of Japan |
| Magazine name: | Journal of Information Processing |
| Volume: | 25 |
| Start page: | 708 |
| End page: | 715 |
| DOI: | 10.2197/ipsjjip.25.708 |
| Abstract: | 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. |
| Rights: | 社団法人 情報処理学会, Takashi Horiyama, Takashi Iizuka, Masashi Kiyomi,Yoshio Okamoto, Ryuhei Uehara, Takeaki Uno, Yushi Uno, and Yukiko Yamauchi, Journal of Information Processing, 25, 2017, 708-715. ここに掲載した著作物の利用に関する注意: 本著作物の著作権は（社）情報処理学会に帰属します。本著作物は著作権者である情報処理学会の許可のもとに掲載するものです。ご利用に当たっては「著作権法」ならびに「情報処理学会倫理綱領」に従うことをお願いいたします。 Notice for the use of this material: The copyright of this material is retained by the Information Processing Society of Japan (IPSJ). This material is published on this web site with the agreement of the author (s) and the IPSJ. Please be complied with Copyright Law of Japan and the Code of Ethics of the IPSJ if any users wish to reproduce, make derivative work, distribute or make available to the public any part or whole thereof. All Rights Reserved, Copyright (C) Information Processing Society of Japan. |
| URI: | http://hdl.handle.net/10119/15060 |
| Material Type: | publisher |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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