Online problems and complexity in games and puzzles

• Project/Area Number: 15K00505
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Entertainment and game informatics 1
• Research Institution: The University of Electro-Communications
• Principal Investigator: Takenaga Yasuhiko 電気通信大学, 大学院情報理工学研究科, 准教授 (20236491)
• Project Period (FY): 2015-10-21 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: ゲーム・パズル / アルゴリズム / 必勝性 / 計算量 / ゲーム / オンライン問題 / 計算複雑さ

Outline of Final Research Achievements

In this research, we deal with a falling block puzzle game PuyoPuyo, which has online property, as a single-player game and consider the conditions so that the player can win, that is, the player can keep playing the game forever on the gameboard of a constant height.
We have considered both the cases that the lookahead of inputs exists as in the real game and it does not exist. In both cases, we have shown sufficient conditions that the player wins and that the player loses using the number of game pieces, the width of the gameboard and the number of lookaheads as parameters. Also we have shown that the ideas of the proofs can be applied to the other similar games.
Also, we have shown algorithms and complexity of the problems to decide if the matchstick puzzles on the grid has a solution and the problem to decide the winner of a tow-player game QUIXO.

Research Products

• [Journal Article] Stgrategies for Single-Player PuyoPuyo (2017)
  • Author(s): Yasuhiko Takenaga and Shimada Yo
  • Journal Title: ICGA Journal Volume: 印刷中 Issue: 2 Pages: 87-101
  • DOI: 10.3233/icg-160001
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] 先読みありの１人ぷよぷよの必勝性 (2017)
  • Author(s): 全 虎山，武永康彦
  • Organizer: 電子情報通信学会総合大会
  • Place of Presentation: 名城大学(愛知県名古屋市）
  • Year and Date: 2017-03-22
• [Presentation] 一人用落ち物パズルゲームの必勝性 (2017)
  • Author(s): 勝野誠基，武永康彦
  • Organizer: 電子情報通信学会総合大会
  • Place of Presentation: 名城大学(愛知県名古屋市）
  • Year and Date: 2017-03-22
• [Presentation] 一般化QUIXOの計算複雑さ (2017)
  • Author(s): 三柴翔平，武永康彦
  • Organizer: 電子情報通信学会総合大会
  • Place of Presentation: 名城大学(愛知県名古屋市）
  • Year and Date: 2017-03-22
• [Presentation] 格子上のマッチ棒パズル (2017)
  • Author(s): 三柴翔平、武永康彦、杉山晴香
  • Organizer: 組合せゲーム・パズルプロジェクト第12回研究集会
  • Place of Presentation: 名古屋大学(愛知県名古屋市）
  • Year and Date: 2017-03-06
• [Presentation] On Winning Strategies for Tetris Type Games (2017)
  • Author(s): Yasuhiko Takenaga, Masaki Katsuno and Hushan Quan
  • Organizer: The 20th Korea-Japan Joint Workshop on Algorithms and Computation
  • Int'l Joint Research
• [Presentation] Matchstick Puzzles on a Grid (2017)
  • Author(s): Yasuhiko Takenaga, Shohei Mishiba and Haruka Sugiyama
  • Organizer: The 20th Japan Conference on Geometry, Graphs, and Games Discrete and Computational
  • Int'l Joint Research
• [Presentation] 得点札を持つ二人トリックテイキングゲームの解析 (2016)
  • Author(s): 金広尚平、武永康彦
  • Organizer: 電子情報通信学会2016年総合大会
  • Place of Presentation: 九州大学
  • Year and Date: 2016-03-15