Game informatics: Search of And-Or tree and Computational Complexity of games and puzzles

2013 Fiscal Year Final Research Report

• Project/Area Number: 23500037
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Software
• Research Institution: The University of Electro-Communications
• Principal Investigator: IWATA Shigeki 電気通信大学, 情報理工学(系)研究科, 教授 (80102028)
• Co-Investigator(Kenkyū-buntansha): TAKENAGA Yasuhoko 電気通信大学, 大学院・情報理工学研究科, 准教授 (20236491) ; KASAI Takumi 電気通信大学, 大学院・情報理工学研究科, 教授 (70027382) ; ITO Hiroo 電気通信大学, 大学院・情報理工学研究科, 教授 (50283487)
• Project Period (FY): 2011 – 2013
• Keywords: ゲーム情報学 / And-Or木の探索 / ゲーム・パズルの複雑さ

Research Abstract

This research is concerned with Game Informatics. The themes are (1) computer search of And-Or trees, and (2) computational complexity of games and puzzles.
Search of And-Or tree (game-tree) by computers generally use evaluation function. We define our game-tree model, and compare numbers of configurations to be searched by depth-first search at the designated depth of our game-tree under various evaluation functions. Our result shows that the number of configurations when an evaluation function is applied, which is as close as the perfect evaluation function with probability p (0<p<1), is polynomial time larger than that of configurations when the perfect evaluation function is applied.
We obtained computational complexities of some games and puzzles, and the results have been published as papers, or presented in international conferences.

Research Products

• [Journal Article] Shikaku and Ripple Effect are NP-complete (2013)
  • Author(s): Yasuhiko Takenaga, Shintaro Aoyagi, Shigeki Iwata, and Takumi Kasai
  • Journal Title: Congressus Numerantium Volume: Vol.216 Pages: 119-127
  • Peer Reviewed
• [Journal Article] Complexity of the stamp folding problem (2013)
  • Author(s): Takuya Umesato, Toshiki Saitoh, Ryuhei Uehara, Hiro Ito, and Yoshio Okamoto
  • Journal Title: Theoretical Computer Science Volume: Vol.497 Pages: 13-19
  • DOI: 10.1016/j.tcs.2012.08.006
  • Peer Reviewed
• [Journal Article] On computational complexity of graph inference from counting (2013)
  • Author(s): Szilard Zsolt Fazekas, Hiro Ito, Yasushi Okuno, Shinnosuke Seki, and Kei Taneishi
  • Journal Title: Natural Computing Volume: Vol.12 Pages: 589-603
  • DOI: 10.1007/s11047-012-9349-2
  • Peer Reviewed
• [Journal Article] Helly numbers of polyominoes (2013)
  • Author(s): Jean Cardinal, Hiro Ito, Matias Korman, and Stefan Langerman
  • Journal Title: Graphs and Combinatorics Volume: Vol.29 Pages: 1221-1234
  • DOI: 10.1007/s00373-012-1203-x
  • Peer Reviewed
• [Journal Article] NP-completeness of two pencil puzzles : Yajilin and Country Road (2012)
  • Author(s): Ayaka Ishibashi, Yuichi Sato, and Shigeki Iwata
  • Journal Title: Utilitas Mathematica Volume: Vol.88 Pages: 237-246
  • Peer Reviewed
• [Journal Article] NP-completeness of Pandemic (2012)
  • Author(s): Kenichiro Nakai, and Yasuhiko Takenaga
  • Journal Title: Journal of Information Processing Volume: Vol.20 Pages: 723-726
  • DOI: 10.2197/ipsjjip.20.723
  • Peer Reviewed
• [Journal Article] トリックテイキングゲームの計算量と必勝戦略 (2012)
  • Author(s): 中井健一朗, 武永康彦
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1799巻 Pages: 183-186
  • Peer Reviewed
• [Presentation] NP-completeness of Kuromasu (2014)
  • Author(s): Yohei Yamaguchi, Yasuhiko Takenaga, and Shigeki Iwata
  • Organizer: 45th Southeastern International Conference on Combinatorics, Graph Theory, and Computing (45th SEICCGTC)
  • Place of Presentation: Florida, U.S.A
  • Year and Date: 20140300
• [Presentation] Shikaku and Ripple Effect are NP-complete (2013)
  • Author(s): Yasuhiko Takenaga, Shintaro Aoyagi, Shigeki Iwata, and Takumi Kasai
  • Organizer: 44th Southeastern International Conference on Combinatorics, Graph Theory, and Computing (44th SEICCGTC)
  • Place of Presentation: Florida, U.S.A
  • Year and Date: 20130300
• [Presentation] How to generalize janken --- rock-paper-scissors-king-flea (2012)
  • Author(s): Hiro Ito
  • Organizer: Proceedings of TJJCCGG
  • Place of Presentation: Bangkok, Thailand
  • Year and Date: 20121200
• [Presentation] Constant-time approximation algorithms for the optimum branching problem on sparse graphs (2012)
  • Author(s): Mitsuru Kusumoto, Yuichi Yoshida, and Hiro Ito
  • Organizer: Proceedings of the Workshop on Computational Complexity Analysis and Algorithm Design for Combinatorial Optimization Problems
  • Place of Presentation: Okinawa, Japan
  • Year and Date: 20121200
• [Presentation] Constant-time algorithms for sparsity matroids (2012)
  • Author(s): Hiro Ito, Shin-ichi Tanigawa, Yuichi Yoshida
  • Organizer: 39th International Colloquium on Automata, Language and Programming (ICALP 2012)
  • Place of Presentation: University of Warwick, UK
  • Year and Date: 20120700
• [Presentation] Algorithms and complexity of generalized river crossing problems (2012)
  • Author(s): Hiro Ito, Stefan Langerman, Yuichi Yoshida
  • Organizer: 6th International Conference on Fun with Algorithms (FUN 2012)
  • Place of Presentation: Venice, Italy
  • Year and Date: 20120600
• [Presentation] Constant-time approximation algorithms for the knapsack problem (2012)
  • Author(s): Hiro Ito, Susumu Kiyoshima, Yuichi Yoshida
  • Organizer: 9th Annual Conference on Theory and Applications of Models of Computation (TAMC 2012)
  • Place of Presentation: Beijing, China
  • Year and Date: 20120500