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Research on the isomorphism for the enumeration of geometric figures

Research Project

Project/Area Number 18K11153
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 60010:Theory of informatics-related
Research InstitutionHokkaido University (2019-2020)
Saitama University (2018)

Principal Investigator

Horiyama Takashi  北海道大学, 情報科学研究院, 教授 (60314530)

Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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 / 二分決定グラフ / 逆探索法 / 包囲多角形 / タイリング
Outline of Final Research Achievements

We focused on the isomorphism, which appears in various problems of computational geometry. We developed isomorphism-elimination algorithms for enumerating geometric objects, and applied the methodology to various fields. The enumeration by our proposed algorithms are based on BDDs (Binary Decision Diagrams) and ZDDs (Zero-suppressed BDDs). By combining the algorithms with the enumeration algorithms with the frontier-method, which is the framework for constructing BDDs/ZDDs in the top-down manner, the enumeration achieves extremely fast speed and extremely small memory consumption. For example, experimental results show that the proposed method is more than 300 times faster and 3,000 times less memory than the conventional algorithm with only the frontier-method.

Academic Significance and Societal Importance of the Research Achievements

本研究課題で取り組んだ同型性の除去は、計算幾何学においてさまざまな問題に横断的に現れる重要な課題である。たとえば、研究代表者がこれまでに幾何図形列挙の応用として取り組んだ、選挙区の区割り問題や、避難所の割当て問題、高分子化合物のトポロジーの列挙などに現れている。こうした諸問題に対し、個別の問題に応じて「何をもって同型とするか」の定義を確認する必要がある。一方で、その先の同型性の除去については、個別に対応を考えるのではなく、それらに共通して必要となる要素を抽出し、同型性をうまく扱うためのアルゴリズム設計の基盤を構築できたことに学術的かつ社会的意義がある。

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (70 results)

All 2021 2020 2019 2018 Other

All Int'l Joint Research (2 results) Journal Article (15 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 15 results,  Open Access: 3 results) Presentation (53 results) (of which Int'l Joint Research: 11 results,  Invited: 6 results)

  • [Int'l Joint Research] MIT(米国)

    • Related Report
      2020 Annual Research Report
  • [Int'l Joint Research] MIT(米国)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Optimal reconfiguration of optimal ladder lotteries2021

    • Author(s)
      Katsuhisa Yamanaka, Takashi Horiyama, Kunihiro Wasa
    • Journal Title

      Theoretical Computer Science

      Volume: 859 Pages: 57-69

    • DOI

      10.1016/j.tcs.2021.01.009

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Enumeration of nonequivalent substitutional structures using advanced data structure of binary decision diagram2020

    • Author(s)
      Shinohara Kohei、Seko Atsuto、Horiyama Takashi、Ishihata Masakazu、Honda Junya、Tanaka Isao
    • Journal Title

      The Journal of Chemical Physics

      Volume: 153 Issue: 10 Pages: 104109-104109

    • DOI

      10.1063/5.0021663

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Rigid Foldability is NP-Hard2020

    • Author(s)
      H. A. Akitaya, E. D. Demaine, T. Horiyama, T. C. Hull, J. S. Ku, T. Tachi,
    • Journal Title

      Journal of Computational Geometry

      Volume: 11(1) Pages: 93-124

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Efficient Algorithm for Box Folding2020

    • Author(s)
      Mizunashi Koichi、Horiyama Takashi、Uehara Ryuhei
    • Journal Title

      Journal of Graph Algorithms and Applications

      Volume: 24 Issue: 2 Pages: 89-103

    • DOI

      10.7155/jgaa.00520

    • NAID

      120006775247

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Sequentially Swapping Colored Tokens on Graphs2019

    • Author(s)
      Katsuhisa Yamanaka, Erik D. Demaine, Takashi Horiyama, Akitoshi Kawamura, Shin-Ichi Nakano, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, and Takeaki Uno
    • Journal Title

      Journal of Graph Algorithms and Applications

      Volume: 23 Issue: 1 Pages: 3-27

    • DOI

      10.7155/jgaa.00482

    • NAID

      120006779053

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Max-Min 3-Dispersion Problems2019

    • Author(s)
      T. Horiyama, S. Nakano, T. Saitoh, K. Suetsugu, A. Suzuki, R. Uehara, T. Uno, K. Wasa
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 11653 Pages: 291-300

    • NAID

      130008081864

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Efficient Segment Folding is Hard2019

    • Author(s)
      T. Horiyama, F. Klute, M. Korman, I. Parada, R. Uehara, K. Yamanaka
    • Journal Title

      Proc. of the 31st Canadian Conference on Computational Geometry

      Volume: 31 Pages: 177-183

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Mind The Mind with Synchronous Clocks2019

    • Author(s)
      T. Horiyama, K. Kurita, Y. Okamoto, K. Uchizawa, R. Uehara
    • Journal Title

      Proc. of the 22nd Japan Conference on Discrete and Computational Geometry, Graphs and Games

      Volume: 22 Pages: 71-72

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Another Representation of Rhombus Tilings2019

    • Author(s)
      T. Horiyama, T. Tachi, A. Tokolo
    • Journal Title

      Proc. of the 22nd Japan Conference on Discrete and Computational Geometry, Graphs and Games

      Volume: 22 Pages: 73-74

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Efficient algorithm for box folding2019

    • Author(s)
      K. Mizunashi, T. Horiyama, R. Uehara
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 11355 Pages: 277-288

    • NAID

      120006775247

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Exact Algorithms for the Max-Min Dispersion Problem2018

    • Author(s)
      T. Akagi, T. Araki, T. Horiyama, S. Nakano, Y. Okamoto, Y. Otachi, T. Saitoh, R. Uehara, T. Uno, K. Wasa
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 10823 Pages: 263-272

    • NAID

      120006648104

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computational Complexity of Robot Arm Simulation Problems2018

    • Author(s)
      T. Feng, T. Horiyama, Y. Okamoto, Y. Otachi, T. Saitoh, T. Uno, R. Uehara
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 10979 Pages: 177-188

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Ladder-Lottery Realization2018

    • Author(s)
      K. Yamanaka, T. Horiyama, T. Uno, K. Wasa
    • Journal Title

      Proc. of the 30th Canadian Conference on Computational Geometry

      Volume: 30 Pages: 61-67

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isomorphism Elimination by Zero-Suppressed Binary Decision Diagrams2018

    • Author(s)
      T. Horiyama, M. Miyasaka, R. Sasaki
    • Journal Title

      Proc. of the 30th Canadian Conference on Computational Geometry

      Volume: 30 Pages: 360-366

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On 2-Dimensional Developments of a 4-Dimensional Hypercube and a Regular Pentachoron2018

    • Author(s)
      T. Horiyama, J. Itoh, C. Nara
    • Journal Title

      Proc. of the 21st Japan Conference on Discrete and Computational Geometry, Graphs and Games

      Volume: 21 Pages: 105-107

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] 動的計画法に基づく Simple Polygonization 列挙アルゴリズムの実験的評価2021

    • Author(s)
      中畑 裕, 堀山 貴史, 湊 真一, 山中 克久
    • Organizer
      情報処理学会アルゴリズム研究会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Efficient Folding Algorithms for Regular Polyhedra2020

    • Author(s)
      T. Kamata, A. Kadoguchi, T. Horiyama, R. Uehara
    • Organizer
      The 32nd Canadian Conference on Computational Geometry
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Enumerating Empty Polygons2020

    • Author(s)
      S. Terui, T. Hirayama, T. Horiyama, K. Yamanaka, T. Uno
    • Organizer
      The 4th International Workshop on Enumeration Problems \& Applications
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 正多面体の折り判定問題の研究2020

    • Author(s)
      鎌田斗南, 門口あきら, 堀山貴史, 上原隆平
    • Organizer
      第28回折り紙の科学・数学・教育研究集会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Enumerating Empty Polygons2020

    • Author(s)
      S. Terui, T. Hirayama, T. Horiyama, K. Yamanaka, T. Uno
    • Organizer
      2020年度電気関係学会東北支部連合大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Sorting by Five Prefix Reversals2020

    • Author(s)
      T. Araki, T. Horiyama, S. Nakano, Y. Okamoto, Y. Otachi, R. Uehara, T. Uno, K. Yamanaka
    • Organizer
      情報処理学会アルゴリズム研究会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Polyhedral Forms from Folding Geodesic Strips2020

    • Author(s)
      S. Nishimoto, T. Horiyama, T. Tachi
    • Organizer
      Virtual Technical Meeting of the Society of Engineering Science 2020
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] コスト制約つき組合せ問題に対するZDDを用いた高速な解列挙手法2020

    • Author(s)
      湊真一, 番原睦則, 堀山貴史, 川原純, 瀧川一学, 山口勇太郎
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 覆面算を列挙するオートマトンの効率的な構築手法2020

    • Author(s)
      渡部航也, ヘンリアン ディプタラマ, 吉仲亮, 堀山貴史, 篠原歩
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 正多面体の折り判定問題の多項式時間解法2020

    • Author(s)
      上原隆平, 門口あきら, 鎌田斗南, 堀山貴史
    • Organizer
      第29回折り紙の科学・数学・教育研究集会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 連結かつ非交差な幾何グラフの列挙,ランダム生成,最適化2020

    • Author(s)
      中畑裕, 堀山貴史, 湊真一, 山中克久
    • Organizer
      LA シンポジウム
    • Related Report
      2019 Research-status Report
  • [Presentation] Efficient Algorithm for Dodecahedron Folding2020

    • Author(s)
      鎌田斗南, 上原隆平, 堀山貴史
    • Organizer
      LA シンポジウム
    • Related Report
      2019 Research-status Report
  • [Presentation] 多面体の展開と折り2020

    • Author(s)
      堀山貴史
    • Organizer
      日本数学会 2020年度年会, 企画特別公演
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Enumeration with Isomorphism Elimination2019

    • Author(s)
      T. Horiyama
    • Organizer
      The 3rd International Workshop on Enumeration Problems & Applications
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Enumeration of Surrounding Polygons2019

    • Author(s)
      K. Yamanaka, T. Horiyama, Y. Okamoto, R. Uehara, T. Yamauchi
    • Organizer
      The 3rd International Workshop on Enumeration Problems & Applications
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Geodesic Folding of Tetrahedron2019

    • Author(s)
      S. Nishimoto, T. Horiyama, T. Tachi
    • Organizer
      Symmetry: Art and Science, 11th Congress and Exhibition
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Mind the Mind with Synchronous Clocks2019

    • Author(s)
      堀山貴史, 栗田和宏, 岡本吉央, 内澤啓, 上原隆平
    • Organizer
      第30回 列挙アルゴリズムセミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] 箱折りのためのアルゴリズム2019

    • Author(s)
      堀山貴史
    • Organizer
      折紙を基礎とする数理と折紙工学への応用発展, 明治大学先端数理科学インスティテュート, MIMS 現象数理学拠点 共同研究集会
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 列挙アルゴリズムの合成による列挙2019

    • Author(s)
      堀山貴史
    • Organizer
      基盤(S) 離散構造処理系プロジェクト 短期滞在セミナー週間 (SSSW) 2019.05
    • Related Report
      2019 Research-status Report
  • [Presentation] ZDD を用いたグラフ細分構造の列挙索引化2019

    • Author(s)
      中畑裕, 川原純, 堀山貴史, 湊真一
    • Organizer
      電子情報通信学会技術研究報告
    • Related Report
      2019 Research-status Report
  • [Presentation] ジオデシック四面体2019

    • Author(s)
      西本清里, 堀山貴史, 舘知宏
    • Organizer
      第26回 折り紙の科学・数学・教育 研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] スポーツスケジューリングにおけるブレーク数上限付きのホーム アウェイ テーブルの列挙 ~アルゴリズムとその実装~2019

    • Author(s)
      中山浩彰, 堀山貴史
    • Organizer
      基盤(S) 離散構造処理系プロジェクト 2019年度 初夏のワークショップ
    • Related Report
      2019 Research-status Report
  • [Presentation] スポーツスケジューリングにおけるブレーク数上限付きの ホームアウェイテーブルの列挙2019

    • Author(s)
      中山浩彰, 堀山貴史
    • Organizer
      第32回 回路とシステムワークショップ
    • Related Report
      2019 Research-status Report
  • [Presentation] スポーツスケジューリングにおけるホームアウェイテーブルの列挙2019

    • Author(s)
      堀山貴史
    • Organizer
      離散数学とその応用研究集会2019
    • Related Report
      2019 Research-status Report
  • [Presentation] Enumeration and Counting of the Developments of Polyhedra2019

    • Author(s)
      T. Horiyama
    • Organizer
      Japanese days at the Laboratory of Informatics, Modelling and Optimization of the Systems
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] アルゴリズムの観点からの展開図作成2019

    • Author(s)
      堀山貴史
    • Organizer
      明治大学アカデミックフェス2019, 数理科学する明治大学
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Enumerating empty polygons2019

    • Author(s)
      S. Terui, T. Hirayama, T. Horiyama, K. Yamanaka
    • Organizer
      令和元年度 情報処理学会 東北支部研究会
    • Related Report
      2019 Research-status Report
  • [Presentation] Enumeration of Surrounding Polygons2019

    • Author(s)
      K. Yamanaka, T. Horiyama, Y. Okamoto, R. Uehara, T. Yamauchi
    • Organizer
      情報系 Winter Festa Episode 5
    • Related Report
      2019 Research-status Report
  • [Presentation] ポリアの数え上げに基づく非同型な塗分けの索引化2019

    • Author(s)
      角野周平, 堀山貴史
    • Organizer
      LA シンポジウム
    • Related Report
      2018 Research-status Report
  • [Presentation] Efficient Algorithm for Box Folding2019

    • Author(s)
      K. Mizunashi, T. Horiyama, R. Uehara
    • Organizer
      LA Symposium
    • Related Report
      2018 Research-status Report
  • [Presentation] ポリアの数え上げに基づく非同型な塗分けの索引化2019

    • Author(s)
      角野周平, 堀山貴史
    • Organizer
      情報処理学会, アルゴリズム研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] Enumerating Surrounding Polygons2019

    • Author(s)
      K. Yamanaka, T. Horiyama, Y. Okamoto, R. Uehara, T. Yamauchi
    • Organizer
      情報処理学会, アルゴリズム研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] Mind the Mind with Synchronous Clocks2019

    • Author(s)
      堀山貴史, 栗田和宏, 岡本吉央, 内澤啓, 上原隆平
    • Organizer
      第14回 組合せゲーム・パズル 研究集会
    • Related Report
      2018 Research-status Report
  • [Presentation] Folding 3D Cell Shapes Optimized by Computational Origami2018

    • Author(s)
      K. Kuribayashi-Shigetomi, T. Horiyama, Q. He, R. Uehara
    • Organizer
      The 7th International Meeting on Origami in Science, Mathematics and Education
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 1-DOF Structure Folding into Multiple Polyhedra2018

    • Author(s)
      T. Tachi, and T. Horiyama
    • Organizer
      The 7th International Meeting on Origami in Science, Mathematics and Education
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] On the Enumeration of the Nonisomorphic Unfoldings of 4-Dimensional Crosspolytopes2018

    • Author(s)
      T. Horiyama, and T. Kondo
    • Organizer
      The 2nd International Workshop on Enumeration Problems & Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Algorithmic Enumeration of Surrounding Polygons2018

    • Author(s)
      K. Yamanaka, T. Horiyama, Y. Okamoto, R. Uehara, T. Yamauchi
    • Organizer
      The 35th European Workshop on Computational Geometry
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] フロンティア法によるDAGの非巡回縮約の列挙2018

    • Author(s)
      中畑 裕, 鈴木 浩史, 石畠 正和, 堀山 貴史
    • Organizer
      2018年度 人工知能学会全国大会
    • Related Report
      2018 Research-status Report
  • [Presentation] ZDD による列挙における同型性の除去2018

    • Author(s)
      堀山貴史
    • Organizer
      離散構造処理系プロジェクト 短期滞在セミナー週間 2018.05
    • Related Report
      2018 Research-status Report
  • [Presentation] 複数の多面体に折れる一自由度機構2018

    • Author(s)
      舘知宏, 堀山貴史
    • Organizer
      第24回 折り紙の科学・数学・教育 研究集会
    • Related Report
      2018 Research-status Report
  • [Presentation] 列挙アルゴリズムとデザイン2018

    • Author(s)
      堀山貴史
    • Organizer
      日本建築学会, 第1回デザイン科学数理知能シンポジウム
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 決定グラフによる禁止マイナー演算2018

    • Author(s)
      中畑裕, 川原純, 堀山貴史, 笠原正治
    • Organizer
      離散構造処理系プロジェクト 2018年度 初夏のワークショップ
    • Related Report
      2018 Research-status Report
  • [Presentation] 決定性有限状態機械による覆面算の列挙2018

    • Author(s)
      野崎裕樹, Diptarama Hendrian, 吉仲亮, 堀山貴史, 篠原歩
    • Organizer
      離散構造処理系プロジェクト 2018年度 初夏のワークショップ
    • Related Report
      2018 Research-status Report
  • [Presentation] 4次元超立方体の2次元展開について2018

    • Author(s)
      堀山貴史
    • Organizer
      MIMS 現象数理学拠点 共同研究集会, 折紙数学と折紙工学を基盤とする産業応用
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 非同型な2端子直並列グラフの列挙とランダムサンプリング2018

    • Author(s)
      伝住周平, 堀山貴史, 栗田和宏, 中畑裕, 鈴木浩史, 和佐州洋, 山崎一明
    • Organizer
      電子情報通信学会, コンピュテーション研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] The Complexity of Ladder-Lottery Realization Problem2018

    • Author(s)
      K. Yamanaka, T. Horiyama, T. Uno, K. Wasa
    • Organizer
      情報処理学会, アルゴリズム研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] グラフに含まれる位相的に同型な部分グラフの列挙索引化2018

    • Author(s)
      中畑裕, 川原純, 堀山貴史, 湊真一
    • Organizer
      離散構造処理系プロジェクト 2018年度 秋のワークショップ
    • Related Report
      2018 Research-status Report
  • [Presentation] スポーツスケジューリングにおけるブレーク数上限付きのホーム アウェイ テーブルの列挙2018

    • Author(s)
      中山浩彰, 堀山貴史
    • Organizer
      離散構造処理系プロジェクト 2018年度 秋のワークショップ
    • Related Report
      2018 Research-status Report
  • [Presentation] 3-Dispersion2018

    • Author(s)
      堀山貴史, 中野眞一, 齋藤寿樹, 末續鴻輝, 鈴木顕, 上原隆平, 宇野毅明, 和佐州洋
    • Organizer
      第29回 列挙アルゴリズムセミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] グラフのユニグラフ分解2018

    • Author(s)
      中畑裕, 川原純, 堀山貴史, 湊真一
    • Organizer
      第29回 列挙アルゴリズムセミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] オイラー路の列挙2018

    • Author(s)
      堀山貴史, 川原純
    • Organizer
      第29回 列挙アルゴリズムセミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] Max-Min 3-dispersion Problems2018

    • Author(s)
      T. Horiyama, S. Nakano, T. Saitoh, K. Suetsugu, A. Suzuki, R. Uehara, T. Uno, K. Wasa
    • Organizer
      電子情報通信学会, コンピュテーション研究会
    • Related Report
      2018 Research-status Report
  • [Presentation] 箱折り問題に対する効率の良いアルゴリズム2018

    • Author(s)
      堀山貴史, 上原隆平, 水無浩一
    • Organizer
      第25回 折り紙の科学・数学・教育 研究集会
    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2022-01-27  

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