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Enumeration of geometric figures and its application

Research Project

Project/Area Number 15K00008
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Horiyama Takashi  埼玉大学, 理工学研究科, 准教授 (60314530)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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 / 選挙区割り / 計算機科学
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). We also applied the methodology to various fields. First, we focused on enumerating the developments of orthogonal boxes. We introduced the notion of unit square development, and proposed an efficient algorithms for constructing ZDDs of the unit square developments. We also considered the problem from the reverse side. That is, we proposed algorithms checking whether a given orthogonal polygon can be folded into an orthogonal box (and giving the creases if possible). As for the application of our method, we have enumerated all patterns of partitions for elections within a disparity bound, and also all rhombille tilings.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (41 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (3 results) Journal Article (16 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 16 results,  Open Access: 4 results,  Acknowledgement Compliant: 3 results) Presentation (22 results) (of which Int'l Joint Research: 9 results,  Invited: 3 results)

  • [Int'l Joint Research] マサチューセッツ工科大学/Western New England University(米国)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] MIT/Western New England University(米国)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] University of British Columbia(カナダ)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Rep-cubes: Dissection of a Cube into Nets2018

    • Author(s)
      Xu Dawei, Huang Jinfeng, Nakane Yuta, Yokoyama Tomoo, Horiyama Takashi, Uehara Ryuhei
    • Journal Title

      IEICE Trans. Fundamentals

      Volume: -

    • NAID

      130007479452

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Enumerating All Spanning Shortest Path Forests with Distance and Capacity Constraints2018

    • Author(s)
      Nakahata Yu, Kawahara Jun, Horiyama Takashi, Kasahara Shoji
    • Journal Title

      IEICE Trans. Fundamentals

      Volume: -

    • NAID

      130007479535

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exact Algorithms for the Max-Min Dispersion Problem2018

    • Author(s)
      Akagi Toshihiro, Araki Tetsuya, Horiyama Takashi, Nakano Shin-Ichi, Okamoto Yoshio, Otachi Yota, Saitoh Toshiki,Uehara Ryuhei, Uno Takeaki, Wasa Kunihiro
    • Journal Title

      Proc. of the 12th International Frontiers of Algorithmics Workshop

      Volume: -

    • NAID

      120006648104

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computational Complexity of Robot Arm Simulation Problems2018

    • Author(s)
      Feng Tianfeng, Horiyama Takashi, Okamoto Yoshio, Otachi Yota, Saitoh Toshiki, Uno Takeaki, Uehara Ryuhei
    • Journal Title

      Proc. of the 29th International Workshop on Combinational Algorithms

      Volume: -

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Common Developments of Three Incongruent Boxes of Area 302017

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

      Computational Geometry: Theory and Applications

      Volume: 印刷中 Pages: 1-17

    • DOI

      10.1016/j.comgeo.2017.03.001

    • NAID

      120005850316

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Sankaku-tori: An Old Western-Japanese Game Played on a Point Set2017

    • Author(s)
      Takashi Horiyama, Takashi Iizuka, Masashi Kiyomi, Yoshio Okamoto, Ryuhei Uehara, Takeaki Uno, Yushi Uno, and Yukiko Yamauchi
    • Journal Title

      Journal of Information Processing

      Volume: 25 Issue: 0 Pages: 708-715

    • DOI

      10.2197/ipsjjip.25.708

    • NAID

      130005990917

    • ISSN
      1882-6652
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complexity of Tiling a Polygon with Trominoes or Bars2017

    • Author(s)
      Takashi Horiyama, Takehiro Ito, Keita Nakatsuka, Akira Suzuki, Ryuhei Uehara
    • Journal Title

      Discrete & Computational Geometry

      Volume: 印刷中 Issue: 3 Pages: 686-704

    • DOI

      10.1007/s00454-017-9884-9

    • NAID

      120006457371

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Rep-cubes: Unfolding and Dissection of Cubes2017

    • Author(s)
      Xu Dawei, Horiyama Takashi, Uehara Ryuhei
    • Journal Title

      Proc. of the 29th Canadian Conference on Computational Geometry

      Volume: 29 Pages: 62-67

    • NAID

      120007005329

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Generating All Patterns of Graph Partitions Within a Disparity Bound2017

    • Author(s)
      J. Kawahara, T. Horiyama, K. Hotta, S. Minato
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 10167 Pages: 119-131

    • DOI

      10.1007/978-3-319-53925-6_10

    • ISBN
      9783319539249, 9783319539256
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Sequentially Swapping Colored Tokens on Graphs2017

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

      Proceedings of 11th International Conference and Workshop on Algorithms and Computation (WALCOM 2017)

      Volume: - Pages: 435-447

    • DOI

      10.1007/978-3-319-53925-6_34

    • NAID

      120006779053

    • ISBN
      9783319539249, 9783319539256
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Continuous Folding of Regular Dodecahedra2016

    • Author(s)
      T. Horiyama, J. Itoh, N. Katoh, Y. Kobayashi, C. Nara
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9943 Pages: 120-131

    • DOI

      10.1007/978-3-319-48532-4_11

    • ISBN
      9783319485317, 9783319485324
    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Box Pleating is Hard2016

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

      Lecture Notes in Computer Science

      Volume: 9943 Pages: 167-179

    • DOI

      10.1007/978-3-319-48532-4_15

    • ISBN
      9783319485317, 9783319485324
    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Convex Configurations on Nana-kin-san Puzzle2016

    • Author(s)
      T. Horiyama, R. Uehara, H. Hosoya
    • Journal Title

      Leibniz International Proceedings in Informatics

      Volume: 49

    • DOI

      10.4230/LIPIcs.FUN.2016.20

    • NAID

      120007005430

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Common Unfolding of Regular Tetrahedron and JZ Solid2016

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

      Journal of Graph Algorithms and Applications

      Volume: 20 Issue: 1 Pages: 101-114

    • DOI

      10.7155/jgaa.00386

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Common Unfolding of Three Different Boxes of Surface Area 302015

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

      Lecture Notes in Computer Science

      Volume: 9076 Pages: 236-247

    • DOI

      10.1007/978-3-319-17142-5_21

    • ISBN
      9783319171418, 9783319171425
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Swapping Colored Tokens on Graphs2015

    • Author(s)
      K. Yamanaka, T. Horiyama, D. Kirkpatrick, Y. Otachi, T. Saitoh, R. Uehara, Y. Uno
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9214 Pages: 619-628

    • DOI

      10.1007/978-3-319-21840-3_51

    • NAID

      120005850327

    • ISBN
      9783319218397, 9783319218403
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Isomorphism Elimination by Zero-Suppressed Binary Decision Diagrams2018

    • Author(s)
      Horiyama Takashi, Miyasaka Masahiro, Sasaki Riku
    • Organizer
      LAシンポジウム
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the Enumeration of the Unfoldings of Hypecubes2018

    • Author(s)
      Horiyama Takashi
    • Organizer
      the 11th Asian Association for Algorithms and Computation Annual Meeting
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the Enumeration of Polymer Topologies2017

    • Author(s)
      T. Haruna, T. Horiyama, K. Shimokawa
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      大分県 由布市
    • Year and Date
      2017-03-13
    • Related Report
      2016 Research-status Report
  • [Presentation] ソーティングネットワークの応用について2017

    • Author(s)
      濱中裕明, 堀山貴史, 上原隆平
    • Organizer
      第25回 列挙アルゴリズムセミナー
    • Place of Presentation
      群馬県 渋川市
    • Year and Date
      2017-02-28
    • Related Report
      2016 Research-status Report
  • [Presentation] 東京2020オリンピック・パラリンピックのエンブレムの多様性について2017

    • Author(s)
      濱中裕明, 堀山貴史, 上原隆平
    • Organizer
      直観幾何学
    • Place of Presentation
      熊本県 熊本市
    • Year and Date
      2017-02-11
    • Related Report
      2016 Research-status Report
  • [Presentation] On the Enumeration of Chequered Tilings in Polygons2017

    • Author(s)
      Hamanaka Hiroaki, Horiyama Takashi, Uehara Ryuhei
    • Organizer
      the 21st Conference of the International Federation of Operational Research Societies
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Enumeration and evaluation for the single-seat constituency system2017

    • Author(s)
      Hotta Keisuke, Kawahara Jun, Horiyama Takashi, Minato Shin-ichi
    • Organizer
      the 21st Conference of the International Federation of Operational Research Societies
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Reconguring Optimal Ladder Lotteries2017

    • Author(s)
      Horiyama Takashi, Wasa Kunihiro, Yamanaka Katsuhisa
    • Organizer
      the 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the Enumeration and Counting of Developments of Polyhedra2016

    • Author(s)
      T. Horiyama
    • Organizer
      International Conference on Mathematical Modeling and Applications 2016 `Origami-Based Modeling and Analysis'
    • Place of Presentation
      東京都 中野区
    • Year and Date
      2016-11-09
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ZDD による組合せ集合の表現と列挙: 基礎から応用へ2016

    • Author(s)
      堀山貴史
    • Organizer
      非線形波動研究の深化と展開
    • Place of Presentation
      福岡県 春日市
    • Year and Date
      2016-11-03
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 逆探索による pmg タイリング可能なポリアモンドの列挙2016

    • Author(s)
      宮坂正大, 堀山貴史
    • Organizer
      情報処理学会アルゴリズム研究会
    • Place of Presentation
      徳島県 徳島市
    • Year and Date
      2016-09-23
    • Related Report
      2016 Research-status Report
  • [Presentation] Folding Orthogonal Polygons into Rectangular Boxes2016

    • Author(s)
      T. Horiyama, K. Mizunashi
    • Organizer
      the 19th Korea-Japan Joint Workshop on Algorithms and Computation
    • Place of Presentation
      北海道 函館市
    • Year and Date
      2016-08-30
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Computational Complexity of Sequential Token Swapping Problem2016

    • Author(s)
      K. Yamanaka, E. D. Demaine, T. Horiyama, A. Kawamura, S. Nakano, Y. Okamoto, T. Saitoh, A. Suzuki, R. Uehara, T. Uno
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Place of Presentation
      石川県 金沢市
    • Year and Date
      2016-06-24
    • Related Report
      2016 Research-status Report
  • [Presentation] 多面体の展開図の列挙について2016

    • Author(s)
      堀山 貴史
    • Organizer
      第29回 回路とシステムワークショップ
    • Place of Presentation
      福岡県 北九州市
    • Year and Date
      2016-05-12
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 直交多角形の直方体折りのための折り線探索2016

    • Author(s)
      堀山貴史, 水無浩一
    • Organizer
      LAシンポジウム
    • Place of Presentation
      京都大学吉田キャンパス (京都府京都市)
    • Year and Date
      2016-01-26
    • Related Report
      2015 Research-status Report
  • [Presentation] 色付きトークン整列問題の計算複雑さ2016

    • Author(s)
      山中克久, 堀山貴史, カークパトリック ディビッド, 大舘陽太, 斎藤寿樹, 上原隆平, 宇野裕之
    • Organizer
      情報処理学会, アルゴリズム研究会
    • Place of Presentation
      湯の原ホテル (宮城県仙台市)
    • Year and Date
      2016-01-21
    • Related Report
      2015 Research-status Report
  • [Presentation] Continuous Folding of Regular Dodecahedra2015

    • Author(s)
      T. Horiyama, J. Itoh, N. Katoh, Y. Kobayashi, C. Nara
    • Organizer
      18th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      京都大学吉田キャンパス (京都府京都市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Box Pleating is Hard2015

    • Author(s)
      J. S. Ku, H. Akitaya, E. D. Demaine, T. Hull, K. C. Cheung, T. Horiyama, T. Tachi, R. Uehara
    • Organizer
      18th Japan Conference on Discrete and Computational Geometry and Graphs
    • Place of Presentation
      京都大学吉田キャンパス (京都府京都市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] m連結成分分割の高速列挙法と区割の比較2015

    • Author(s)
      川原 純, 堀田 敬介, 堀山 貴史, 湊 真一
    • Organizer
      日本オペレーションズ・リサーチ学会 2015年秋季研究発表会
    • Place of Presentation
      九州工業大学戸畑キャンパス (福岡県北九州市)
    • Year and Date
      2015-09-10
    • Related Report
      2015 Research-status Report
  • [Presentation] Ls in L and Sphinxes in Sphinx2015

    • Author(s)
      T. Horiyama, Y. Okamoto, R. Uehara
    • Organizer
      18th Korea-Japan Joint Workshop on Algorithms and Computation
    • Place of Presentation
      Songdo Convensia, Incheon, Korea
    • Year and Date
      2015-08-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Ls in L and Sphinxes in Sphinx2015

    • Author(s)
      T. Horiyama, Y. Okamoto, R. Uehara
    • Organizer
      LAシンポジウム
    • Place of Presentation
      ゆのくに天祥 (石川県加賀市)
    • Year and Date
      2015-07-16
    • Related Report
      2015 Research-status Report
  • [Presentation] フロンティア法による連結成分列挙と選挙制度への応用2015

    • Author(s)
      堀田 敬介, 川原 純, 堀山 貴史, 湊 真一
    • Organizer
      日本選挙学会 研究会
    • Place of Presentation
      市民会館崇城大学ホール (熊本県熊本市)
    • Year and Date
      2015-05-17
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2022-02-16  

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