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

Research Project

Project/Area Number 23500037
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Software
Research InstitutionThe 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
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsゲーム情報学 / And-Or木の探索 / ゲーム・パズルの複雑さ / ゲーム木のモデル / 深さ優先探索 / 評価関数 / パズルの計算複雑性 / And-Or木
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.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (30 results)

All 2014 2013 2012 Other

All Journal Article (17 results) (of which Peer Reviewed: 17 results) Presentation (13 results)

  • [Journal Article] Shikaku and Ripple Effect are NP-complete2013

    • Author(s)
      Yasuhiko Takenaga, Shintaro Aoyagi, Shigeki Iwata, and Takumi Kasai
    • Journal Title

      Congressus Numerantium

      Volume: Vol.216 Pages: 119-127

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The complexity of the stamp folding problem2013

    • Author(s)
      Takuya Umesato, Toshiki Saitoh, Ryuhei Uehara, Hiro Ito, and Yoshio Okamoto
    • Journal Title

      Theoretical Computer Science

      Volume: -- Pages: 13-19

    • DOI

      10.1016/j.tcs.2012.08.006

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] On computational complexity of graph inference from counting2013

    • Author(s)
      Szilard Zsolt Fazekas, Hiro Ito, Yasushi Okuno, Shinnosuke Seki, and Kei Taneishi
    • Journal Title

      Natural Computing

      Volume: Vol.12 Issue: 4 Pages: 589-603

    • DOI

      10.1007/s11047-012-9349-2

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Helly numbers of polyominoes2013

    • Author(s)
      Jean Cardinal, Hiro Ito, Matias Korman, and Stefan Langerman
    • Journal Title

      Graphs and Combinatorics

      Volume: Vol.29 Issue: 5 Pages: 1221-1234

    • DOI

      10.1007/s00373-012-1203-x

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Constant-time approximation algorithms for the optimum branching problem on sparse graphs2013

    • Author(s)
      Mitsuru Kusumoto, Yuichi Yoshida, and Hiro Ito
    • Journal Title

      International Journal of Networking and Computing

      Volume: 3 Pages: 201-216

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] How to generalize janken --- rock-paper-scissors-king-flea2013

    • Author(s)
      Hiro Ito
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8296 Pages: 85-94

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] NP-completeness of two pencil puzzles : Yajilin and Country Road2012

    • Author(s)
      Ayaka Ishibashi, Yuichi Sato, and Shigeki Iwata
    • Journal Title

      Utilitas Mathematica

      Volume: Vol.88 Pages: 237-246

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] NP-Completeness of Pandemic2012

    • Author(s)
      Kenichiro Nakai, and Yasuhiko Takenaga
    • Journal Title

      Journal of Information Processing

      Volume: 20 Issue: 3 Pages: 723-726

    • DOI

      10.2197/ipsjjip.20.723

    • NAID

      130002116383

    • ISSN
      1882-6652
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • 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

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] NP-completeness of two pencil puzzles: Yajilin and Country Road2012

    • Author(s)
      Ayaka Ishibashi, Yuichi Sato, and Shigeki Iwata
    • Journal Title

      Utilitas Mathematica

      Volume: 88 Pages: 237-246

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] トリックテイキング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 Pages: 183-186

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Constant-time approximation algorithms for the knapsack problem2012

    • Author(s)
      Hiro Ito, Susumu Kiyoshima, Yuichi Yoshida
    • Journal Title

      Proc. of The 9th Annual Conference on Theory and Applications of Models of Computation (TAMC 2012), LNCS

      Volume: 7287 Pages: 131-142

    • NAID

      110008689181

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Algorithms and complexity of generalized river crossing problems2012

    • Author(s)
      Hiro Ito, Stefan Langerman, Yuichi Yoshida
    • Journal Title

      Proc. of The 6th International Conference on Fun with Algorithms (FUN 2012), LNCS

      Volume: 7288 Pages: 235-244

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Constant-time algorithms for sparsity matroids2012

    • Author(s)
      Hiro Ito Shin-ichi Tanigawa, Yuichi Yoshida
    • Journal Title

      Proc. of The 39th International Colloquium on Automata, Language and Programming (ICALP 2012) (1), LNCS

      Volume: 7391 Pages: 498-509

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] NP-completeness of Two Pencil Puzzles: Yajilin and Country Road2012

    • Author(s)
      Ayaka Ishibashi, Yuichi Sato, and Shigeki Iwata
    • Journal Title

      Utilitas Mathematica

      Volume: 掲載予定

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] NP-completenes of Pandemic2012

    • Author(s)
      Kenichiro Nakai and Yasuhiko Takenaga
    • Journal Title

      Journal of Information Processing

      Volume: 掲載予定

    • Related Report
      2011 Research-status Report
    • 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: 掲載予定

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] NP-completeness of Kuromasu2014

    • 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
    • Related Report
      2013 Final Research Report
  • [Presentation] NP-completeness of Kuromasu2014

    • 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 Atlantic University
    • Related Report
      2013 Annual Research Report
  • [Presentation] Shikaku and Ripple Effect are NP-complete2013

    • 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
    • Related Report
      2013 Final Research Report
  • [Presentation] 上書きハッシュ表の性質2013

    • Author(s)
      山口 陽平, 岩田 茂樹
    • Organizer
      第12回情報科学技術フォーラム(FIT2013)
    • Place of Presentation
      鳥取大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Shikaku and Ripple effect are NP-complete2013

    • Author(s)
      Yasuhiko Takenaga, Shintaro Aoyagi, Shigeki Iwata, and Takumi Kasai
    • Organizer
      Forty-fourth Southeastern Conference on Combinatorics, Graph Thery and Computing
    • Place of Presentation
      Florida Atlantic University, Boca Raton, Florida, USA
    • Related Report
      2012 Research-status Report
  • [Presentation] How to generalize janken --- rock-paper-scissors-king-flea2012

    • Author(s)
      Hiro Ito
    • Organizer
      Proceedings of TJJCCGG
    • Place of Presentation
      Bangkok, Thailand
    • Related Report
      2013 Final Research Report
  • [Presentation] Constant-time approximation algorithms for the optimum branching problem on sparse graphs2012

    • 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
    • Related Report
      2013 Final Research Report
  • [Presentation] Constant-time algorithms for sparsity matroids2012

    • 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
    • Related Report
      2013 Final Research Report
  • [Presentation] Algorithms and complexity of generalized river crossing problems2012

    • Author(s)
      Hiro Ito, Stefan Langerman, Yuichi Yoshida
    • Organizer
      6th International Conference on Fun with Algorithms (FUN 2012)
    • Place of Presentation
      Venice, Italy
    • Related Report
      2013 Final Research Report
  • [Presentation] Constant-time approximation algorithms for the knapsack problem2012

    • 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
    • Related Report
      2013 Final Research Report
  • [Presentation] Constant-time approximation algorithms for the optimum branching problem on sparse graphs2012

    • Author(s)
      Mitsuru Kusumoto, Yuichi Yoshida, and Hiro Ito
    • Organizer
      Workshop on Computational Complexity Analysis and Algorithm Design for Combinatorial Optimization Problems (WCOP) in ICNC'12
    • Place of Presentation
      Okinawa, Japan
    • Related Report
      2012 Research-status Report
  • [Presentation] 3点タイル張り問題の解の列挙2012

    • Author(s)
      田中成俊、羽原貴広、武永康彦
    • Organizer
      第7回組合せゲーム・パズルミニ研究集会
    • Place of Presentation
      大阪商業大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 色数と盤面の幅を限定したぷよぷよの必勝性

    • Author(s)
      島田陽,武永康彦
    • Organizer
      組合せゲーム・パズル第9回ミニ研究集会
    • Place of Presentation
      北陸先端科学技術大学院大学
    • Related Report
      2013 Annual Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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