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On the enumeration of geometric objects

Research Project

Project/Area Number 24500008
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Fundamental theory of informatics
Research InstitutionSaitama University

Principal Investigator

HORIYAMA Takashi  埼玉大学, 情報メディア基盤センター, 准教授 (60314530)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsアルゴリズム / 列挙アルゴリズム / 計算幾何学 / 展開図 / 多面体 / タイリング
Outline of Final Research Achievements

The methodology for designing enumeration algorithms of geometric objects are discussed by integrating basic technologies (e.g., BDDs (Binary Decision Diagrams), ZDDs (Zero-suppressed BDDs) and reverse search). As for the enumeration of developments of polyhedra, the efficiency of the combined method with the frontier-based ZDD construction and a removal of isomorphic developments is shown. The extension of this method is discussed for enumerating general developments (i.e., developments obtained by cutting not only the edges but also faces) of polyhedra. Moreover, the counting method for essentially different developments of any polyhedron is proposed. We can count the number of non-isomorphic developments without enumerating the developments.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (41 results)

All 2015 2014 2013 2012 Other

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (31 results) Book (1 results)

  • [Journal Article] Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid2015

    • Author(s)
      Y. Araki, T. Horiyama, R. Uehara
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8973 Pages: 294-305

    • NAID

      120005893623

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Common Developments of Three Incongruent Boxes of Area 302015

    • Author(s)
      D. Xu, T. Horiyama, T. Shirakawa, R. Uehara
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9076 Pages: 236-247

    • NAID

      120005850316

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational Complexity of Piano-Hinged Dissections2014

    • Author(s)
      Z. Abel, E. D. Demaine, M. L. Demaine, T. Horiyama, R. Uehara
    • Journal Title

      IEICE Trans. Fundamentals

      Volume: E97-A Pages: 1206-1212

    • NAID

      130004770850

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Base-object location problems for base-monotone regions2014

    • Author(s)
      J. Chun, T. Horiyama, T. Ito, N. Kaothanthong, H. Ono, Y. Otachi, T. Tokuyama, R. Uehara, T. Uno
    • Journal Title

      Theoretical Computer Science

      Volume: 555 Pages: 71-84

    • NAID

      120005851303

    • Related Report
      2014 Annual Research Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sankaku-Tori: An Old Western-Japanese Game Played on a Point Set2014

    • Author(s)
      T. Horiyama, M. Kiyomi, Y. Okamoto, R. Uehara, T. Uno, Y. Uno, Y. Yamauchi
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8496 Pages: 230-239

    • NAID

      120005850326

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Number of Different Unfoldings of Polyhedra2013

    • Author(s)
      T. Horiyama, W. Shoji
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8283 Pages: 623-633

    • DOI

      10.1007/978-3-642-45030-3_58

    • NAID

      110009569455

    • ISBN
      9783642450297, 9783642450303
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Base Location Problems for Base-Monotone Regions2013

    • Author(s)
      Jinhee Chun, Takashi Horiyama, Takehiro Ito, Natsuda Kaothanthong, Hirotaka Ono, Yota Otachi, Takeshi Tokuyama, Ryuhei Uehara, Takeaki Uno
    • Journal Title

      7^<th> International Workshop on Algorithms and Computation

      Volume: 7748 Pages: 53-64

    • DOI

      10.1007/978-3-642-36065-7_7

    • ISBN
      9783642360640, 9783642360657
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Automatic Multi-Stage Clock Gating Optimization Using ILP Formulation2012

    • Author(s)
      X. Man, T. Horiyama, S. Kimura
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E95.A Issue: 8 Pages: 1347-1358

    • DOI

      10.1587/transfun.E95.A.1347

    • NAID

      10031126653

    • ISSN
      0916-8508, 1745-1337
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Packing Trominoes is NP-Complete, #P-hard and ASP-Complete2012

    • Author(s)
      T. Horiyama, T. Ito, K. Nakatsuka, A. Suzuki, R. Uehara
    • Journal Title

      Proc. of the 24th Canadian Conference on Computational Geometry

      Volume: 24 Pages: 219-224

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Swapping Colored Tokens on Graphs2015

    • Author(s)
      K. Yamanaka, T. Horiyama, D. Kirkpatrick, Y. Otachi, T. Saitoh, R. Uehara, Y. Uno
    • Organizer
      The Algorithms and Data Structures Symposium
    • Place of Presentation
      University of Victoria, BC, Canada
    • Year and Date
      2015-08-05 – 2015-08-07
    • Related Report
      2014 Annual Research Report
  • [Presentation] 面積30の3つの箱の共通の展開図2014

    • Author(s)
      D. Xu, 堀山貴史, 白川俊博, 上原隆平
    • Organizer
      第17回 折り紙の科学・数学・教育 研究集会
    • Place of Presentation
      東京都文京区, JOASホール
    • Year and Date
      2014-12-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] 空間充填立体 bar-joint フレームワークの最適なブレース追加手法2014

    • Author(s)
      小林祐貴, 伊藤慈彦, 東川雄哉, 加藤直樹, 堀山貴史, 伊藤仁一, 奈良知恵
    • Organizer
      電子情報通信学会 コンピュテーション研究会
    • Place of Presentation
      熊本県熊本市, 崇城大学
    • Year and Date
      2014-12-05
    • Related Report
      2014 Annual Research Report
  • [Presentation] Optimally Bracing Frameworks of Union of Space-lling Convex Polyhedra2014

    • Author(s)
      Y. Ito, Y. Kobayashi, Y. Higashikawa, N. Katoh, T. Horiyama, J. Itoh, C. Nara
    • Organizer
      17th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      東京都新宿区, 東京理科大学 神楽坂キャンパス
    • Year and Date
      2014-09-16
    • Related Report
      2014 Annual Research Report
  • [Presentation] Common Unfolding of Regular Tetrahedron and Johnson-Zalgaller Solid2014

    • Author(s)
      Y. Araki, T. Horiyama, R. Uehara
    • Organizer
      情報処理学会 アルゴリズム研究会
    • Place of Presentation
      山形県米沢市, 伝国の杜
    • Year and Date
      2014-09-12
    • Related Report
      2014 Annual Research Report
  • [Presentation] 一つ、二つ、たくさん ~列挙アルゴリズムの入門から応用まで~ [招待講演]2014

    • Author(s)
      堀山貴史
    • Organizer
      情報オリンピック 夏季セミナー
    • Place of Presentation
      東京都渋谷区, 国立オリンピック記念青少年総合センター
    • Year and Date
      2014-08-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] 逆探索に基づく pmg タイリングの列挙2014

    • Author(s)
      西岡潤, 堀山貴史
    • Organizer
      第27回 回路とシステムワークショップ
    • Place of Presentation
      兵庫県淡路市, 淡路夢舞台国際会議場
    • Year and Date
      2014-08-05
    • Related Report
      2014 Annual Research Report
  • [Presentation] Enumeration of All Paths Between All Pairs of Vertices by Zero-Suppressed Binary Decision Diagrams2014

    • Author(s)
      T. Horiyama, K. Adachi
    • Organizer
      20th Conference of the International Federation of Operational Research Societies
    • Place of Presentation
      Barcelona, Spain
    • Year and Date
      2014-07-13
    • Related Report
      2014 Annual Research Report
  • [Presentation] 正四面体が折れるジョンソン・ザルガラー立体の辺展開図について2014

    • Author(s)
      荒木義明, 堀山貴史, 上原隆平
    • Organizer
      第16回 折り紙の科学・数学・教育 研究集会
    • Place of Presentation
      東京都文京区, JOASホール
    • Year and Date
      2014-06-22
    • Related Report
      2014 Annual Research Report
  • [Presentation] pmg タイリング可能なポリオミノの列挙2014

    • Author(s)
      西岡潤, 堀山貴史
    • Organizer
      電子情報通信学会 コンピュテーション研究会
    • Place of Presentation
      愛媛県松山市, 大和屋本店
    • Year and Date
      2014-06-14
    • Related Report
      2014 Annual Research Report
  • [Presentation] Enumeration of Polyominoes for p4 Isohedral Tiling Revisited2014

    • Author(s)
      T. Horiyama, S. Yamane
    • Organizer
      7th Asian Association for Algorithms and Computation Annual Meeting
    • Place of Presentation
      Hangzhou, China
    • Year and Date
      2014-05-17
    • Related Report
      2014 Annual Research Report
  • [Presentation] Sankaku-Tori: An Old Western-Japanese Game Played on a Point Set2014

    • Author(s)
      T. Horiyama, M. Kiyomi, Y. Okamoto, R. Uehara, T. Uno, Y. Uno, Y. Yamauchi
    • Organizer
      7th International Conference on Fun with Algorithms
    • Place of Presentation
      Sicily, Italy
    • Related Report
      2013 Research-status Report
  • [Presentation] Enumeration of All Paths between All Pairs of Vertices by Zero-Suppressed Binary Decision Diagrams2014

    • Author(s)
      T. Horiyama, K. Adachi
    • Organizer
      20th Conference of the International Federation of Operational Research Societies
    • Place of Presentation
      Barcelona, Spain
    • Related Report
      2013 Research-status Report
  • [Presentation] Enumeration of region partitioning for evacuation planning based on ZDD2013

    • Author(s)
      A. Takizawa, Y. Takechi, A. Ohta, N. Katoh, T. Inoue, T. Horiyama, J. Kawahara, S. Minato
    • Organizer
      11th International Symposium on Operations Research and its Applications in engineering, technology and management
    • Place of Presentation
      Huangshan, China
    • Related Report
      2013 Research-status Report
  • [Presentation] Computational Complexity of Piano-Hinged Dissections2013

    • Author(s)
      Z. Abel, E. D. Demaine, M. L. Demaine, T. Horiyama, R. Uehara
    • Organizer
      情報処理学会, アルゴリズム研究会
    • Place of Presentation
      小樽市, 小樽商科大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ZDD-Based Approach to Solving Tantrix

    • Author(s)
      Y. Hagiwara, T. Horiyama, Y. Uno
    • Organizer
      6th Asian Association for Algorithms and Computation Annual Meeting
    • Place of Presentation
      松島市, 松島大観荘
    • Related Report
      2013 Research-status Report
  • [Presentation] The Number of Different Unfoldings of Polyhedra

    • Author(s)
      T. Horiyama, W. Shoji
    • Organizer
      24th International Symposium on Algorithms and Computation
    • Place of Presentation
      the University of Hong Kong, Hong Kong
    • Related Report
      2013 Research-status Report
  • [Presentation] Enumerating Polyominoes of p4 Tiling Revisited

    • Author(s)
      T. Horiyama, S. Yamane
    • Organizer
      LA symposium
    • Place of Presentation
      京都市, 京都大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 正多面体の展開図のパッキング問題について

    • Author(s)
      堀山貴史, 古岡泰成
    • Organizer
      第9回 組合せゲーム・パズル 研究集会
    • Place of Presentation
      能美市, 北陸先端科学技術大学院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 三角取りの多項式時間解法とNP完全性の研究

    • Author(s)
      堀山貴史, 清見礼, 岡本吉央, 上原隆平, 宇野毅明, 宇野裕之, 山内由紀子
    • Organizer
      第9回 組合せゲーム・パズル 研究集会
    • Place of Presentation
      能美市, 北陸先端科学技術大学院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ZDD を用いた都市の避難所割り当ての列挙

    • Author(s)
      瀧澤重志, 武知祥史, 大田章雄, 中野浩太郎, 加藤直樹, 井上武, 堀山貴史, 川原純, 湊真一
    • Organizer
      日本オペレーションズ・リサーチ学会 2013年秋季研究発表会
    • Place of Presentation
      徳島市, 徳島大学
    • Related Report
      2013 Research-status Report
  • [Presentation] The Number of Edge Unfoldings of the Archimedean Solids

    • Author(s)
      T. Horiyama, W. Shoji
    • Organizer
      5th Asian Association for Algorithms and Computation Annual Meeting
    • Place of Presentation
      Fudan University, Shanghai, P.R.China
    • Related Report
      2012 Research-status Report
  • [Presentation] 多面体の非同型な展開図の個数について

    • Author(s)
      堀山貴史, 庄子亘
    • Organizer
      情報処理学会, アルゴリズム研究会
    • Place of Presentation
      松山市, 愛媛大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Packing Trominoes is NP-Complete, #P-Complete and ASP-Complete

    • Author(s)
      T. Horiyama, T. Ito, K. Nakatsuka, A. Suzuki, R. Uehara
    • Organizer
      LA Symposium
    • Place of Presentation
      宮津市, 宮津ロイヤルホテル
    • Related Report
      2012 Research-status Report
  • [Presentation] Packing Trominoes is NP-Complete, #P-hard and ASP-Complete

    • Author(s)
      T. Horiyama, T. Ito, K. Nakatsuka, A. Suzuki, R. Uehara
    • Organizer
      24th Canadian Conference on Computational Geometry
    • Place of Presentation
      Charlottetown, Prince Edward Island, Canada
    • Related Report
      2012 Research-status Report
  • [Presentation] 多面体の展開図の列挙と索引化について

    • Author(s)
      堀山貴史
    • Organizer
      学習理論における組合せ論ワークショップ
    • Place of Presentation
      福岡市, 九州大学
    • Related Report
      2012 Research-status Report
  • [Presentation] On the Complexity of Packing Trominoes

    • Author(s)
      T. Horiyama, T. Ito, K. Nakatsuka, A. Suzuki, R. Uehara
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      仙台市, 東北大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Algorithms for Computing Optimal Image Segmentation using Quadtree Decomposition

    • Author(s)
      J. Chun, T. Horiyama, T. Ito, N. Kaothanthong, H. Ono, Y. Otachi, T. Tokuyama, R. Uehara, T. Uno
    • Organizer
      Thailand-Japan Joint Conference on Computational Geometry and Graphs
    • Place of Presentation
      Srinakharinwirot University, Bangkok, Thailand
    • Related Report
      2012 Research-status Report
  • [Presentation] Base location problems for base-monotone regions

    • Author(s)
      J. Chun, T. Horiyama, T. Ito, N. Kaothanthong, H. Ono, Y. Otachi, T. Tokuyama, R. Uehara, T. Uno
    • Organizer
      7th International Workshop on Algorithms and Computation
    • Place of Presentation
      Indian Institute of Technology, Kharagpur, India
    • Related Report
      2012 Research-status Report
  • [Presentation] The Number of Different Unfoldings of Polyhedra

    • Author(s)
      T. Horiyama, W. Shoji
    • Organizer
      29th European Workshop on Computational Geometry
    • Place of Presentation
      TU Braunschweig, Braunschweig, Germany
    • Related Report
      2012 Research-status Report
  • [Presentation] Computational Complexity of Piano-Hinged Dissections

    • Author(s)
      Z. Abel, E. D. Demaine, M. L. Demaine, T. Horiyama, R. Uehara
    • Organizer
      29th European Workshop on Computational Geometry
    • Place of Presentation
      TU Braunschweig, Braunschweig, Germany
    • Related Report
      2012 Research-status Report
  • [Book] 社会のさまざまな問題への応用 (超高速グラフ列挙アルゴリズム 〈フカシギの数え方〉が拓く, 組合せ問題への新アプローチ 8章)2015

    • Author(s)
      堀山貴史
    • Publisher
      森北出版
    • Related Report
      2014 Annual Research Report

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Published: 2013-05-31   Modified: 2019-07-29  

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